Exhibit 4.1

FIRST AMENDMENT TO RIGHTS AGREEMENT

THIS FIRST AMENDMENT TO RIGHTS AGREEMENT (this “First Amendment”), dated as of January 24, 2005, by and between Cheniere Energy, Inc., a Delaware corporation (the “Company”), and U.S. Stock Transfer Corp., as Rights Agent (the “Rights Agent”), constitutes the first amendment to that certain Rights Agreement, dated October 14, 2004, by and between the Company and the Rights Agent (the “Rights Agreement”).

W I T N E S S E T H:

WHEREAS, the parties hereto desire to amend the Rights Agreement in certain respects on the terms and conditions hereinafter set forth;

NOW, THEREFORE, in consideration of the premises and for other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, the parties hereto do hereby agree as follows:

1. Amendment of Rights Agreement. Section 7(b) of the Rights Agreement is hereby amended by substituting the dollar amount of “$700” for the amount of “$200” stated therein.

2. Defined Terms. All terms defined in the Rights Agreement that are used herein shall have the meanings so defined in the Rights Agreement, unless specifically noted otherwise herein.

3. Complete Agreement. The term “Agreement” or “Rights Agreement” as used in the Rights Agreement shall mean the Rights Agreement, as amended by this First Amendment, or as it may, from time to time, be amended in the future by one or more other written amendment or modification agreements entered into pursuant to Section 27 of the Rights Agreement. This First Amendment is not intended to be, nor shall it be construed to be, a novation.

4. Binding Agreement. This First Amendment shall be binding upon and shall inure to the benefit of the parties hereto and their respective successors and assigns.

5. Governing Law. This First Amendment shall be governed by, construed and enforced in accordance with the laws of the State of Delaware, without reference to its conflicts of laws principles.

6. Effectiveness. This First Amendment is effective as of the date first written above. Except as expressly herein amended, the terms and conditions of the Rights Agreement are hereby ratified and remain in full force and effect.

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IN WITNESS WHEREOF, the parties hereto have caused this First Amendment to be duly executed as of the date first above written.

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