FIRST AMENDMENT TO EMPLOYMENT AGREEMENT

Exhibit 10.26

PLAINS EXPLORATION & PRODUCTION COMPANY

FIRST AMENDMENT TO

EMPLOYMENT AGREEMENT

WHEREAS, effective as of June 9, 2004, Plains Exploration & Production Company (the “Company”) entered into an employment agreement (the “Agreement”) with Stephen A. Thorington (the “Employee”); and

WHEREAS, the Company and the Employee have agreed to amend the Agreement as set forth below;

NOW, THEREFORE, the Company and the Employee agree as follows:

1. Paragraph 4(b) of the Agreement shall be amended by adding the following sentence thereto:

“Such bonus, if any, shall be paid not later than the fifteenth day of the third calendar month following the later of (i) the last day of the calendar year or (ii) the last day of the Company’s fiscal year in which the calendar year ends.”

2. Paragraph 6(c)(ix) shall be added to the Agreement to read as follows:

“Notwithstanding the foregoing or anything herein to the contrary, if any amounts payable hereunder are reasonably determined by the Company to be “nonqualified deferred compensation” payable to a “specified employee” upon “separation from service” (within the meaning of section 409A of the Internal Revenue Code of 1986 as amended and any applicable regulations or other guidance issued pursuant thereto (the “Code”)) then such amounts shall not be paid upon separation from service, but shall be paid as described below. As soon as administratively feasible upon the Employee’s separation from service, or, if earlier, upon a Change of Control, the maximum amount which may become payable to Employee after separation from service shall be contributed to the trustee of a “rabbi” trust substantially in the form attached hereto (the “Trust”). Such amounts that would otherwise be payable upon separation from service shall be held by the trustee pursuant to the terms of such Trust and paid to Employee as soon as administratively feasible following the earlier of: (1) the first day that is six months following his separation from service; or (2) Employee’s date of death. Such amounts that would otherwise be payable in installments commencing on separation from service shall be accumulated and paid in a lump sum on the date that is the earlier of (1) or (2) above and shall be paid in installments thereafter.”

3. Paragraph 6(h) of the Agreement shall be amended to read as follows: