Exhibit 10.71

Execution Version

FIRST AMENDMENT TO INVESTORS’ AGREEMENT

THIS FIRST AMENDMENT TO INVESTORS’ AGREEMENT, dated as of November 11, 2008 (this “Amendment”), is among Cheniere Energy, Inc., a Delaware corporation (including successors, the “Company”), Cheniere Common Units Holding, LLC, a Delaware limited liability company (the “Borrower”), and GSO Special Situations Fund LP, GSO Origination Funding Partners LP, Blackstone Distressed Securities Fund L.P., GSO COF Facility LLC, and Scorpion Capital Partners LP (collectively, the “Investors”, and each, an “Investor”).

RECITALS

WHEREAS, the Company, the Borrower and the Investors are parties to an Investors’ Agreement dated as of August 15, 2008 (as amended, modified or supplemented from time to time, the “Investors’ Agreement”).

WHEREAS, the parties to the Investors’ Agreement desire to amend the Investors’ Agreement as contemplated herein to modify the time period within which the Company is required to prepare and file a registration statement as set forth below.

NOW, THEREFORE, in consideration of the foregoing and the mutual agreements set forth in this Amendment, the Company, the Borrower and the Investors agree as follows:

1. Defined Terms. Unless otherwise defined herein, capitalized terms used herein have the meanings assigned to such terms in the Investors’ Agreement.

2. Amendment to Investors’ Agreement. Section 4.8.1 of the Investors’ Agreement shall be amended and restated in its entirety to read as follows:

“4.8.1 (a) With respect to a registration pursuant to Section 4.1, prepare and file, within forty-five (45) days of receipt of written notice from the majority of Holders, and (b) with respect to a registration pursuant to Section 4.2 (to the extent the Company has not fulfilled the requirements of the foregoing clause (a) and as provided in Section 4.1), prepare and file, within ninety (90) days of receipt of written notice from the Initiating Holders pursuant to Section 4.2, in each case with the SEC a Registration Statement with respect to such Registrable Securities, make all required filings with the Financial Industry Regulatory Authority and thereafter use its commercially reasonable efforts to cause such Registration Statement to become effective as soon as reasonably practicable and to remain effective as provided herein; provided that, before filing a Registration Statement or any amendments or supplements thereto, the Company will, at the Company’s expense, furnish or otherwise make available to the Holders’ Counsel copies of all such documents proposed to be filed and such other documents reasonably requested by such counsel, which documents will be subject to the review and reasonable comment of such counsel at the Company’s expense, including any comment letter from the SEC with respect to such filing or the

documents incorporated by reference therein, and if requested by such counsel, provide such counsel reasonable opportunity to participate in the preparation of such Registration Statement and such other opportunities to conduct a reasonable investigation within the meaning of the Securities Act, including reasonable access to the Company’s financial books and records, officers, accountants and other advisors;”.

3. Conditions Precedent. The effectiveness of this Amendment is subject to the satisfaction of the following conditions precedent:

(a) Amendment. The Investors shall have received duly executed and delivered counterparts of this Amendment that, when taken together, bear the signatures of the Company, the Borrower and the Holders that beneficially own a majority of the voting Registrable Securities beneficially owned by all Holders on and as of the date hereof.

(b) Representations and Warranties. The representations and warranties set forth in Section 4 below shall be true and correct in all material respects on and as of the date hereof.

4. Representations and Warranties. The Company and the Borrower hereby jointly and severally represent and warrant to the each Investor that:

(a) Authorization, No Conflicts. The execution, delivery and performance of this Amendment by each of the Company, the Borrower and the Investors (i) has been duly authorized by all requisite corporate, partnership or limited liability company and, if required, stockholder, partner or member action of such person and (ii) will not (A) violate (1) any provision of law, statute, rule or regulation, or of the certificate or articles of incorporation or other constitutive documents or by-laws of such person, (2) any order of any Governmental Authority or arbitrator or (3) any provision of any indenture, agreement or other instrument to which such person is a party or by which it or any of its property is or may be bound or (B) be in conflict with, result in a breach of or constitute (alone or with notice or lapse of time or both) a default under, or give rise to any right to accelerate or to require the prepayment, repurchase or redemption of any obligation under any such indenture, agreement or other instrument.

(b) Enforceability. This Amendment has been duly executed and delivered by each of the Company, the Borrower and the Investors and constitutes a legal, valid and binding obligation of each such person enforceable against such person in accordance with its terms, subject to applicable bankruptcy, insolvency, reorganization, moratorium or other laws affecting creditors’ rights generally and subject to general principles of equity, regardless of whether considered in a proceeding in equity or at law.

5. Continuing Effect of the Investors’ Agreement. This Amendment does not constitute a waiver of any provision of the Investors’ Agreement and is not to be construed as a consent to any action on the part of the Borrower or the Company that would require a waiver or consent of the Investors or an amendment or modification to

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any term of the Investors’ Agreement, except as expressly stated herein. Each of the Company, the Borrower and the Investors hereby confirms and ratifies the Investors’ Agreement as amended hereby and acknowledges and agrees that the same continue in full force and effect as amended hereby (as applicable).

6. Reference to the Investors’ Agreement. Upon the effectiveness of this Amendment, each reference in the Investors’ Agreement to “this Agreement,” “hereunder,” “herein” or words of like import refer to the Investors’ Agreement, as amended and affected hereby.

7. Arm’s Length/Good Faith. This Amendment has been negotiated at arm’s length and in good faith by the parties hereto.

8. Counterparts. This Amendment may be executed by all parties hereto in any number of counterparts (including by facsimile or other electronic transmission), each of which shall be an original and all of which taken together shall constitute one and the same agreement.

9. References. The words “hereby,” “herein,” “hereinabove,” “hereinafter,” “hereinbelow,” “hereof,” “hereunder” and words of similar import when used in this Amendment refer to this Amendment as a whole and not to any particular article, section or provision of this Amendment.

10. Severability. If any provision of this Amendment is held by a court of competent jurisdiction to be invalid or unenforceable in any jurisdiction, such holding shall not affect the validity or enforceability of the remainder of this Amendment in such jurisdiction or the validity or enforceability of this Amendment, including such provision, in any other jurisdiction, and such provision shall be revised or modified to the minimum degree necessary to render it valid and enforceable.

11. Headings Descriptive. Headings should be ignored in construing this Amendment.

12. Governing Law. This Amendment and the rights and obligations of the parties hereunder and the Persons subject hereto shall be governed by and construed and interpreted in accordance with the laws of the State of Delaware, without giving effect to conflicts of laws rules that would require or permit the application of the laws of another jurisdiction.

13. WAIVER OF JURY TRIAL. EACH PARTY TO THIS AMENDMENT ACKNOWLEDGES AND AGREES THAT ANY CONTROVERSY THAT MAY ARISE UNDER THIS AMENDMENT IS LIKELY TO INVOLVE COMPLICATED AND DIFFICULT ISSUES, AND THEREFORE EACH SUCH PARTY HEREBY IRREVOCABLY AND UNCONDITIONALLY WAIVES ANY RIGHT SUCH PARTY MAY HAVE TO A TRIAL BY JURY IN RESPECT OF ANY LITIGATION DIRECTLY OR INDIRECTLY ARISING OUT OF OR RELATING TO THIS AMENDMENT, OR THE BREACH, TERMINATION OR VALIDITY OF THIS AMENDMENT, OR THE

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TRANSACTIONS CONTEMPLATED BY THIS AMENDMENT OR THE INVESTORS’ AGREEMENT. EACH SUCH PARTY CERTIFIES AND ACKNOWLEDGES THAT (A) NO REPRESENTATIVE, AGENT OR ATTORNEY OF ANY OTHER PARTY HAS REPRESENTED, EXPRESSLY OR OTHERWISE, THAT SUCH OTHER PARTY WOULD NOT, IN THE EVENT OF LITIGATION, SEEK TO ENFORCE THE FOREGOING WAIVER, (B) EACH SUCH PARTY UNDERSTANDS AND HAS CONSIDERED THE IMPLICATIONS OF THIS WAIVER, (C) EACH SUCH PARTY MAKES THIS WAIVER VOLUNTARILY AND (D) EACH SUCH PARTY HAS BEEN INDUCED TO ENTER INTO THIS AMENDMENT BY, AMONG OTHER THINGS, THE MUTUAL WAIVERS AND CERTIFICATIONS IN THIS SECTION 13.

14. Final Agreement of the Parties. This Amendment and the Investors’ Agreement, together with the Credit Agreement and related documents, constitute the entire agreement and understanding of the parties hereto with respect to the matters referred to herein and supersede all prior agreements, understandings or representations, written or oral, and all contemporaneous oral agreements, understandings or representations, in each case among the parties with respect to such matters.

[Signature Pages Follow]

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IN WITNESS WHEREOF, the parties are signing this Amendment as of the date first above written.

Signature Page to First Amendment to Investors’ Agreement

Signature Page to First Amendment

Signature Page to First Amendment