FIRST AMENDMENT TO THE DYNEGY INC.

Exhibit 10.4

[EXECUTION ORIGINAL]

FIRST AMENDMENT TO THE DYNEGY INC.

DEFERRED COMPENSATION PLAN FOR CERTAIN DIRECTORS

WHEREAS, Dynegy Inc. (the “Company”) has heretofore established the Dynegy Inc. Deferred Compensation Plan For Certain Directors (the “Plan”);

WHEREAS, the Company has heretofore amended and restated the Plan effective as of January 1, 2003;

WHEREAS, the Company desires to amend the Plan;

WHEREAS, Section 9 of the Plan provides that the Company’s Board of Directors (the “Board”) may amend the Plan at any time; and

WHEREAS, on May 19, 2005, the Board adopted a resolution providing for the amendment of the Plan as set forth herein;

NOW THEREFORE, the Plan is hereby amended as follows, effective as of July 1, 2005:

1. The first sentence of Section 2 of the Plan is amended in its entirety to provide as follows:

“On each March 31, June 30, September 30 and December 31 that occurs after the Effective Date, the Company shall credit to a Company deferral account maintained by the Company on behalf of each Participant (a ‘Company Deferral Account’) a number of hypothetical shares (including fractional shares) of Class A common stock, without par value, of the Company (‘Common Stock’) equal to (a) $15,000.00 divided by (b) the closing price of a share of Common Stock on the last Trading Day (as hereinafter defined) of the calendar quarter ending on such March 31, June 30, September 30 or December 31, as applicable; provided, however, that a Participant’s Company Deferral Account shall receive such credit only if such Participant was a director of the Company on the March 31, June 30, September 30 or December 31 to which such credit relates or his or her service as a director of the Company terminated during the calendar quarter ending on such date by reason of death or disability.”

2. Except as modified herein, the Plan shall remain in full force and effect.

EXECUTED this 15th day of September, 2005.

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