Exhibit 10.5

EXECUTION COPY

EQUITY CONTRIBUTION AGREEMENT

Dated as of May 13, 2015

among

CHENIERE CORPUS CHRISTI HOLDINGS, LLC,

and

CHENIERE ENERGY, INC.

TABLE OF CONTENTS

(i)

EQUITY CONTRIBUTION AGREEMENT

This EQUITY CONTRIBUTION AGREEMENT (this “Agreement”), dated as of May 13, 2015, is between CHENIERE CORPUS CHRISTI HOLDINGS, LLC, a Delaware limited liability company (the “Company”), and CHENIERE ENERGY, INC., a Delaware corporation (“Parent”).

RECITALS

A. Corpus Christi Liquefaction, LLC (“CCL”), a direct wholly-owned subsidiary of the Company and an indirect wholly-owned subsidiary of Parent, intends to develop, construct, operate, maintain and own facilities in San Patricio County and Nueces County in the vicinity of Portland, Texas, on the La Quinta Channel in the Corpus Christi Bay, which will have as the initial phase, the development of two Trains, two LNG storage tanks and one marine berth and as the second phase, the development of an additional Train, LNG storage tank and marine berth, with each Train with a nominal production capacity of approximately 4.5 mtpa and each LNG storage tank with a working capacity of 160,000 cubic meters, and Gas pretreatment and processing facilities and certain onsite and offsite utilities and supporting infrastructure (the “Corpus Christi Terminal Facility”);

B. Cheniere Corpus Christi Pipeline, L.P. (“CCP”), a direct wholly-owned subsidiary of the Company and an indirect wholly-owned subsidiary of Parent, intends to develop, construct, operate, maintain and own a 23-mile-long, 48-inch-diameter bi-directional Gas pipeline and related compressor stations, meter stations and required interconnects, originating at the Corpus Christi Terminal Facility and terminating north of the City of Sinton, Texas, and related facilities, designed to transport up to a maximum of 2.25 Bcf/d of feed and fuel gas to the Corpus Christi Terminal Facility from the existing Gas pipeline grid (which pipeline facilities, together with the Corpus Christi Terminal Facility, as such facilities may be improved, replaced, modified, changed or expanded in accordance with the Finance Documents, the “Project Facilities”);

C. To finance the development of the Project Facilities, the Company intends to incur senior secured debt pursuant to a Common Terms Agreement, dated as of May 13, 2015, among the Company, CCL, CCP, CCP GP and Société Générale, as the Term Loan Facility Agent on behalf of itself and the Term Lenders and as the Intercreditor Agent for the Facility Lenders, and each other Facility Agent on behalf of itself and on behalf of the Facility Lenders under its Facility Agreement from time to time (the “Common Terms Agreement”) and related Finance Documents, and it is a condition to Closing (as defined in the Common Terms Agreement) that this Agreement shall have been executed and be in full force and effect;

D. The Company and Parent desire to enter into this Agreement in order to set out certain provisions regarding, among other things, the obligation of Parent to provide certain equity funding to the Company.

NOW, THEREFORE, in consideration of the foregoing, and for other good and valuable consideration, the receipt and adequacy of which are acknowledged, the parties agree as follows:

1. Definitions. Unless the context otherwise requires, or unless otherwise defined in this Agreement, capitalized terms used in this Agreement have the meanings assigned to those terms in the Common Terms Agreement and will be interpreted according to Section 1 of the Common Terms Agreement. In addition, the terms set out below have the respective meanings given to such terms below.

“Cash Equity Funding” means cash contributions made, directly or indirectly, to the Company by Parent or an Affiliate of Parent.

“Equity Discharge Date” means the later to occur of (a) the date on which the Company has received, directly or indirectly, from Parent the First Tier Equity Funding Amount and (b) the earlier of the Project Completion Date and the date on which the Company has received, directly or indirectly, from Parent the Maximum Second Tier Pro Rata Equity Funding.

“First Tier Equity Funding Amount” means an aggregate amount of Cash Equity Funding equal to (a) unless and until the Second Phase CP Date has occurred, the Phase One First Tier Equity Funding Amount plus (b) on and following the Second Phase CP Date, the Phase Two First Tier Equity Funding Amount. For the avoidance of doubt, unless and until the Second Phase CP Date has occurred, the First Tier Equity Funding Amount will not include the Phase Two First Tier Equity Funding Amount.

“Phase One First Tier Equity Funding Amount” means $1,499 million, which amount may be increased at any time by Parent at its sole discretion by sending a written notice to the Company specifying the incremental amount of Cash Equity Funding to be included within the Phase One First Tier Equity Funding Amount.

“Phase Two First Tier Equity Funding Amount” means the incremental amount of first-tier equity funding specified in a written notice delivered by Parent to the Company on or prior to the Second Phase CP Date, which amount shall in no event be less than $122 million but may be higher than such amount as specified in the Base Case Forecast under line item K96 (Equity Tranche 1 – Upfront Equity (Stage 2)) delivered under Section 4.3(g) (Conditions to Second Phase Expansion – Base Case Forecast) of the Common Terms Agreement.

“Maximum Second Tier Pro Rata Equity Funding” means an aggregate amount of Cash Equity Funding to be made available following the contribution of the First Tier Equity Funding Amount in accordance with this Agreement equal to either (a) unless and until the Second Phase CP Date has occurred, a total aggregate amount of $1,137 million or (b) on and following the Second Phase CP Date, the amount of second tier pro rata equity funding specified in a written notice delivered by Parent to the Company on or prior to the Second Phase CP Date, which amount shall equal the lesser of (x) $1,137 million and (y) the total aggregate amount of the second tier pro rata equity funding specified in the Base Case Forecast under line item K97 (Equity Tranche 2 – Pro-rata Equity) delivered under Section 4.3(g) (Conditions to Second Phase Expansion – Base Case Forecast) of the Common Terms Agreement.

2. First Tier Equity Funding Amount.

(a) Parent hereby irrevocably agrees to provide Cash Equity Funding to the Company in an amount equal to the First Tier Equity Funding Amount in accordance with this Agreement.

(b) On the date or dates specified by the Company in one or more requests for funds delivered by the Company to Parent, Parent shall pay or cause to be paid to the Company Cash Equity Funding in amounts from time to time up to the First Tier Equity Funding Amount such that the Company shall have received (i) the full Phase One First Tier Equity Funding Amount by the date on which all other conditions to the Initial Advance under the Common Terms Agreement are satisfied (or waived in accordance with the Finance Documents) and (ii) the full Phase Two First Tier Equity Funding Amount as of the Second Phase CP Date. For the avoidance of doubt, Parent shall not be required to pay or cause to be paid the Phase Two First Tier Equity Funding Amount unless and until the Second Phase CP Date has occurred.

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3. Second Tier Equity Funding.

(a) Parent hereby irrevocably agrees to provide Cash Equity Funding to the Company in an amount equal to the Maximum Second Tier Pro Rata Equity Funding in accordance with this Agreement.

(b) Except as provided in clause (d) below, on the date or dates specified by the Company in one or more requests for funds delivered by the Company to Parent following the date of the Initial Advance, where immediately preceding the requested funding date of the Cash Equity Funding, the Company has (or after giving effect to the applicable Advance of Senior Debt, will have) a Senior Debt/Equity Ratio of greater than 75:25 and the Company so specifies in its funding request, Parent shall pay or cause to be paid to the Company Cash Equity Funding in amounts up to the Maximum Second Tier Pro Rata Equity Funding in order to satisfy the requirement in Section 3(c) below.

(c) Except as provided in clause (d) below, it is intended that the Cash Equity Funding paid or caused to be paid by Parent to the Company pursuant to Section 3(b) shall be funded at such times and in such manner concurrently with Advances of Senior Debt such as to enable the Company to achieve and maintain a Senior Debt/Equity Ratio of no greater than 75:25.

(d) At any time following:

(i) the date on which the Initial Advance under the Term Loan Facility Agreement has occurred until the Project Completion Date, following a Loan Facility Declared Default and, except to the extent such acceleration is stayed or prevented due to the Bankruptcy of a Loan Party, the acceleration of any Senior Debt pursuant to the Finance Documents, in each case that is Continuing, at the written demand of the Security Trustee, Parent shall, within 10 Business Days, pay or cause to be paid to the Security Trustee for deposit in the Enforcement Proceeds Account or Construction Account as instructed by the Security Trustee, all remaining Cash Equity Funding required to reach the Maximum Second Tier Pro Rata Equity Funding; and

(ii) the date on which the First Tier Equity Funding Amount is paid or caused to be paid to the Company until the Project Completion Date, in the event of a Parent Bankruptcy, Parent shall, within 10 Business Days, pay or cause to be paid to the Company all remaining Cash Equity Funding required to reach the Maximum Second Tier Pro Rata Equity Funding.

4. Funding Requirements.

(a) Parent shall pay or cause to be paid all Cash Equity Funding required to be paid or caused to be paid by it under Sections 2 and 3 by wire transfer of immediately available funds to the Equity Proceeds Account pursuant to Section 4.5(b) of the Common Security and Account Agreement, for application in accordance with the Common Security and Account Agreement other than as set forth in Section 3(d) above; provided that with respect to any portion of the

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Cash Equity Funding that is to be used to pay any fees concurrently with the signing of the Finance Documents or Closing or Initial Advance of Senior Debt, Parent may direct the payment of such portion of the Cash Equity Funding to the Term Loan Facility Agent on the Company’s behalf.

(b) Capital contributions made to satisfy Cash Equity Funding obligations under this Agreement will be made on account of equity interests previously issued, and neither Parent nor any Subsidiary or Affiliate of Parent shall be entitled to receive, and the Company will not be required to issue, new equity interests.

5. Absolute Obligation; Waivers.

(a) The obligations of Parent under Sections 2, 3 and 4 are absolute and unconditional under any and all circumstances, including the existence of any obligation or indebtedness owing by either the Company (or its subsidiaries) or Parent to Parent or any Affiliate of Parent (cumulatively, the “Cheniere Group”) or of any set-off, counterclaim, recoupment, defense or other right or claim that any member of the Cheniere Group may have against any other member of the Cheniere Group or any other Person, the dissolution, bankruptcy, insolvency or reorganization of the Company or any other member of the Cheniere Group, or any other Person or the pendency against the Company or any other member of the Cheniere Group, or any other Person of any case, suit or proceeding under any bankruptcy or insolvency law or any other law providing for the relief of debtors or any other circumstances whatsoever that might otherwise constitute an excuse for non-performance of the obligations of Parent under Sections 2, 3 or 4, whether similar or dissimilar to any of the circumstances herein specified. Parent hereby unconditionally and irrevocably waives and relinquishes, to the maximum extent permitted by applicable Laws, all of the following rights and remedies and agrees not to assert or take advantage of any such rights or remedies, including:

(i) any right to require the Security Trustee or the Senior Creditors to proceed against the Company, or any other Person or to proceed against or exhaust any security or Collateral held by the Security Trustee or any other Senior Creditors at any time or to pursue any other remedy in the Security Trustee’s or any other Senior Creditor’s power before proceeding against Parent;

(ii) any defense that may arise by reason of the lack of power or authority, dissolution, merger or termination of Parent, the Company, or any other Person or the failure of the Security Trustee or any other Senior Creditor to file or enforce a claim against the estate (in administration, a Bankruptcy Proceeding or any other proceeding) of Parent, the Company, or any other Person;

(iii) any defense based on any offset against any amounts that may be owed by the Loan Parties to Parent for any reason whatsoever;

(iv) promptness, diligence, demand, presentment, protest and notice of any kind (other than any notices required hereby), including notice of any action or non-action on the part of the Company, the Security Trustee, Senior Creditors, any endorser or creditor of the foregoing, or on the part of any other Person under this or any other instrument in connection

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with any obligation or evidence of indebtedness held by the Security Trustee or the Senior Creditors as Collateral or in connection with any amounts due under this Agreement or any other Finance Document;

(v) any defense of setoff or counterclaim that may at any time be available to or asserted by the Company or any Affiliates of the Company against the Security Trustee, the Senior Creditors or any other Person under any Finance Document;

(vi) any duty on the part of the Security Trustee or any Senior Creditors to disclose to Parent any facts any Senior Creditors may now or hereafter know about the Company or the Project;

(vii) any defense based on any change in the time, manner or place of any payment or performance under, or in any other term of, any Finance Document, or any other amendment, renewal, extension, acceleration, compromise or waiver of or any consent or departure from the terms of any Finance Document; and

(viii) any defense arising by reason of any bankruptcy, insolvency, reorganization, arrangement, readjustment of debt, liquidation or dissolution proceeding commenced by or against any Person, including any discharge of, or bar or stay against collecting, all or any part of the amounts due under this Agreement or any other Finance Document (or any interest on all or any part of the amounts due under this Agreement or any other Finance Document) in or as a result of any such proceeding, any failure of the Security Trustee to file a claim in any such proceeding, or the occurrence of any of the following: (i) the election by the Security Trustee, in any bankruptcy proceeding of any Person, of the application or non-application of Section 1111(b)(2) of the Bankruptcy Code, (ii) any extension of credit or the grant of any lien or encumbrance under Section 364 of the Bankruptcy Code, (iii) any use of cash collateral under Section 363 of the Bankruptcy Code, or (iv) any agreement or stipulation with respect to the provision of adequate protection in any bankruptcy proceeding of any Person.

(b) The obligations of Parent to contribute or cause to be contributed Cash Equity Funding as provided in Sections 2, 3 or 4 will not be affected by any default by the Loan Parties in the performance or observance of any of their agreements or covenants in any of the Finance Documents to which any of them are party; will not be subject to any abatement, reduction, limitation, impairment, termination, set-off, defense, counterclaim or recoupment whatsoever or any right to any thereof; and will not be released, discharged or in any way affected by any reorganization, arrangement, compromise or plan affecting any Loan Party, or by any compromise, settlement, release, modification, amendment (whether material or otherwise), waiver or termination of any or all of the obligations, conditions, covenants or agreements of any Person in respect of any of the Finance Documents; or by the occurrence of any Unmatured Loan Facility Event of Default, Loan Facility Event of Default or other default or event of default under the Finance Documents; or by the taking or omission of any action referred to in any of the Finance Documents; or by the exchange, surrender, substitution or modifications of any security for the Senior Debt; or by any lack of validity or enforceability of the Finance Documents, whether or not Parent has notice or knowledge of any of the foregoing.

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(c) Without limitation of the foregoing clause (a) or (b) of this section, Parent hereby irrevocably waives, to the extent it may do so under the law, any protection to which it may be entitled under Sections 365(c)(1), 365(c)(2) and 365(e)(2) of the Bankruptcy Code or equivalent provisions of the laws of any other jurisdiction with respect to any proceedings, or any successor provision of law of similar import, in the event of any Bankruptcy with respect to the Company. Specifically, in the event that the trustee (or similar official) in a Bankruptcy with respect to the Company or the debtor-in-possession takes any action (including the institution of any action, suit or other proceeding for the purpose of enforcing the rights of the Company, under this Agreement or any other Finance Document), Parent shall not assert any defense, claim or counterclaim denying liability hereunder on the basis that this Agreement or any other Finance Document is an executory contract or a “financial accommodation” that cannot be assumed, assigned or enforced or on any other theory directly or indirectly based on Sections 365(c)(1), 365(c)(2) or 365(e)(2) of the Bankruptcy Code, or equivalent provisions of the law of any other jurisdiction with respect to any proceedings or any successor provision of law of similar import. If a Bankruptcy with respect to the Company shall occur, Parent agrees, after the occurrence of such Bankruptcy, to reconfirm in writing, to the extent permitted by applicable laws, its pre-petition waiver of any protection to which it may be entitled under Sections 365(c)(1), 365(c)(2) and 365(e)(2) of the Bankruptcy Code or equivalent provisions of the laws of any other jurisdiction with respect to proceedings and, to give effect to such waiver, Parent consents, to the fullest extent it may do so under applicable law, to the assumption and enforcement of each provision of this Agreement and any other Finance Document by the debtor-in-possession or the trustee in bankruptcy of the Company.

6. Representations and Warranties of Parent. On the date hereof and on the date of each Cash Equity Funding advance made pursuant to Sections 2, 3 and 4, Parent represents and warrants as follows:

(a) It is a corporation duly incorporated, validly existing and in good standing under the laws of the State of Delaware.

(b) It has full corporate power and authority to execute and deliver, and to perform its obligations under, this Agreement. The execution, delivery and performance by it of this Agreement have been duly authorized by all necessary corporate action on its part. This Agreement has been duly executed and delivered by it and (assuming the due execution and delivery by the counterparty hereto) is in full force and effect and constitutes its legal, valid and binding obligation, enforceable against it in accordance with its terms, except as limited by general principles of equity and bankruptcy, insolvency and similar laws.

(c) The execution and delivery of this Agreement and the performance by it of this Agreement in all material respects do not and will not require any consent or approval of any Person that has not been obtained, which consent or approval (to the extent obtained) remains in full force and effect;

(d) The execution, delivery and performance by it of this Agreement do not and will not:

(i) violate any of the terms or provisions of Parent’s Constitutional Documents in any material respect;

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(ii) constitute a default under any agreement, instrument or arrangement to which it is a party or by which it or any of Parent’s properties or assets are bound (in each case which is material to the conduct of its business);

(iii) violate any material Government Rule;

(iv) violate any provision of any Permit applicable to Parent or the Project (in each case which is material to the conduct of the Parent’s business or the Project); or

(v) result in, or create any Lien (other than a Permitted Lien) upon or with respect to any of the properties now owned or hereafter acquired by the Company.

7. Amendments, Etc. No amendment or waiver of any provision of this Agreement, nor consent to any departure by any party hereto therefrom, will, in any event, be effective unless in writing and signed by all parties hereto, and then such waiver or consent will be effective only in the specific instance and for the specific purpose for which given.

8. Notices. Any notice, claim, request, demand, consent, designation, direction, instruction, certificate, report or other communication to be given under or in connection with this Agreement must be given in writing and will be deemed duly given when (i) personally delivered; (ii) sent by facsimile transmission (with transmittal confirmation or acknowledgment of receipt, whether written or oral); (iii) sent by electronic mail (with electronic confirmation of receipt); or (iv) five days have elapsed after mailing by certified or registered mail, postage pre-paid, return receipt requested, in each case addressed to a Person at its address, e-mail address, or facsimile transmission number as indicated in Schedule 1 hereto or to such other address, e-mail address, or facsimile transmission number of which such Person has given notice. Each party may change its address, facsimile or telephone number for notices and other communications hereunder by notice to the other parties hereto.

9. No Waiver; Remedies. No failure on the part of the Company to exercise, and no delay in exercising, any right hereunder will operate as a waiver thereof; nor will any single or partial exercise of any right hereunder preclude any other or further exercise thereof or the exercise of any other right. The remedies herein provided are cumulative and not exclusive of any remedies provided by law.

10. Continuing Agreement. This Agreement is a continuing agreement and will (i) remain in full force and effect until the Equity Discharge Date, (ii) be binding upon the Company and Parent and their respective permitted successors and assigns and (iii) inure to the benefit of and be enforceable by the Company and Parent and their respective permitted successors, transferees and assigns.

11. Assignment; Transfer.

(a) Neither the Company nor Parent may assign or be released from its obligations hereunder without the consent of the other parties hereto. Parent expressly acknowledges that the Company has pledged and assigned all of its rights under this Agreement to secure the Senior Debt Obligations.

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(b) No transfer or assignment by Parent of all or any portion of its direct or indirect equity interests in the Company will relieve Parent of its obligations under this Agreement.

12. Limitation of Liability . Subject to Section 3(d), neither Parent nor any of its Affiliates (other than the Company, Holdco, CCL, CCP and CCP GP, in each case solely in accordance with the Finance Documents) will be personally liable for payments of Senior Debt Obligations or any other amounts or liabilities due under the Finance Documents or for the performance of any obligation thereunder.

13. Remedies Cumulative. Each and every right and remedy of the Company is, to the extent permitted by law, cumulative and is in addition to any other remedy given hereunder or now or hereafter existing at law or in equity or by statute.

14. Governing Law. This Agreement shall be governed by and construed in accordance with the laws of the State of New York, United States, without regard to conflicts of laws principles thereof that would result in the application of the law of any other jurisdiction.

15. Waiver of Jury Trial. Each party hereto hereby waives, to the fullest extent permitted by applicable law, any and all right to trial by jury in any legal proceeding arising out of or relating to this Agreement, the Finance Documents or the transactions contemplated thereby.

16. Consent to Jurisdiction.

(a) Each party hereto, as contemplated by Section 14 shall consent to the non-exclusive jurisdiction of the courts of the State of New York (except as otherwise specifically provided herein).

(b) Each party hereto:

(i) hereby irrevocably consents and agrees that the federal or state courts in the Borough of Manhattan, the City of New York shall have jurisdiction over any legal action, suit or proceeding against it with respect to its obligations, liabilities or any other matter under or arising out of, or in connection with, this Agreement and the Loans;

(ii) irrevocably waives any objection it may now or hereafter have to the laying of venue of any action or proceeding in any such court and any claim it may now or hereafter have that any action or proceeding has been brought in an inconvenient forum; and

(iii) irrevocably consents and agrees that the submission to the jurisdiction of the federal or state courts in the Borough of Manhattan, the City of New York shall not limit the rights of the parties hereto to bring any action or proceeding in any other court of competent jurisdiction nor shall the bringing of any action or the taking of any proceedings in any other jurisdiction (whether concurrently or not) limit such rights, in each case, to the extent permitted by applicable law.

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(c) Without prejudice to any other mode of service allowed under any relevant law, the Company:

(i) agrees that failure by a process agent to notify it of the process will not invalidate the proceedings concerned;

(ii) shall maintain a duly appointed and authorized agent for service of process in relation to any proceedings before the federal or state courts of the Borough of Manhattan, the City of New York in connection with this Agreement and shall keep the Intercreditor Agent advised of the identity and location of such agent and acknowledges that it shall appoint Corporation Service Company (CSC) as its agent for service of process at its registered office (being, on the Signing Date, at 1180 Avenue of the Americas, Suite 210, New York, NY 10036-8401); and

(iii) shall irrevocably authorize the Intercreditor Agent to appoint an agent for service of process on its behalf should it at any time fail to maintain in full force and effect a process agent in accordance with this Section 16.

(d) Each of the parties hereto agrees that upon service of process to the Company’s agent for service of process appointed for such purpose under clause (c) above, a copy of such process shall be delivered to the Company, in accordance with the procedure for notices set forth in Schedule 1 attached hereto, provided that the non-delivery of such copy shall not affect the enforceability of such process validly served upon such agent.

17. Counterparts. This Agreement may be executed in counterparts (and by different parties in different counterparts), each of which will constitute an original, but all of which when taken together will constitute a single contract. Delivery of an executed counterpart of a signature page of this Agreement by facsimile or portable document format (“pdf”) will be effective as delivery of a manually executed counterpart of this Agreement.

[Signatures on following pages]

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IN WITNESS WHEREOF, the parties hereto have caused this Agreement to be duly executed and delivered by their respective officers thereunto duly authorized as of the date first above written.