THIRD AMENDMENT TO THE SECOND SUPPLEMENT TO THE DYNEGY INC. EXECUTIVE SEVERANCE PAY PLAN

Exhibit 10.4

THIRD AMENDMENT TO THE

SECOND SUPPLEMENT TO THE

DYNEGY INC. EXECUTIVE SEVERANCE PAY PLAN

WHEREAS, Dynegy Inc. (the “Company”) and certain subsidiaries and affiliated entities have heretofore established the Dynegy Inc. Executive Severance Pay Plan (the “Plan”);

WHEREAS, the Company has heretofore adopted the Second Supplement to the Dynegy Inc. Executive Severance Pay Plan (the “Second Supplement”) on behalf of itself and all of its subsidiaries and affiliated entities that participate in the Plan;

WHEREAS, the Company has adopted an amendment (the “First Amendment”) to the Second Supplement;

WHEREAS, the Company maintains certain plans under which stock options have been granted to eligible employees (the “Stock Option Plans”);

WHEREAS, the Company desires to amend the Second Supplement on behalf of itself and its participating subsidiaries and affiliated entities in order to clarify that the First Amendment was not intended to restrict any discretionary power or authority provided for in the Stock Option Plans, including, without limitation, the power or authority to make any changes to or (together with any appropriate payment, if applicable, provided for in the relevant plan) cancellations of outstanding stock options in connection with a change in control; and

WHEREAS, Section 4.3 of the Second Supplement provides that the Board of Directors of the Company (or the Compensation Committee of the Board) may amend the Second Supplement;

NOW, THEREFORE, the Second Supplement is hereby amended as follows, effective as of June 22, 2005:

1. Section 3.1(c) of the Second Supplement is amended in its entirety to provide as follows:

“All of the Covered Individual’s outstanding stock options, restricted stock awards, phantom stock and other equity-based awards previously granted by his Employer(s) shall become fully vested and immediately exercisable in full on the date of a Change in Control and such stock options shall remain exercisable from such date for the lesser of: (1) five (5) years from the date of such a Change in Control; (2) the remaining period of time for exercise of such stock options under the option
agreement(s) pursuant to which such stock options were granted (irrespective of any mandatory exercise period specified therein that would otherwise be triggered by the termination of employment of such Covered Individual); or (3) such period of time (which period of time may

end as early as the consummation of a Change in Control) as the Board of Directors may determine in connection with or in contemplation of a Change in Control in the exercise of its discretion under the applicable stock option plans, with respect to which the Board of Directors has the discretion to, among other things, require the surrender of stock options (which surrender may be in exchange for a cash payment, if applicable) and to cancel such stock options upon the consummation of a Change in Control as further described in the applicable stock option plans;”

2. Section 4.12 of the Second Supplement is amended in its entirety to provide as follows:

“4.12 Equity-Based Awards. This Section 4.12 applies only to Covered Individuals whose employment is not subject to an Involuntary Termination. Covered Individuals whose employment is subject to an Involuntary Termination are subject to the provisions of Subsection 3.1(c) hereof. Any outstanding stock options, restricted stock awards, phantom stock and other equity-based awards previously granted to a Covered Individual by his Employer(s) shall immediately vest upon a Change in Control involving a Covered Individual’s Principal Business Unit (but only with respect to Principal Business Unit Covered Individuals) or, in the alternative, a Change in Control involving Dynegy Inc. (with respect to all Covered Individuals). With respect to any outstanding stock options vested pursuant to this Section 4.12, such stock options shall remain fully exercisable by such Covered Individuals for the lesser of: (1) five (5) years from the date of such a Change in Control, provided, that in the case of a Change in Control involving Dynegy Inc., such exercise period shall not be subject to the five-year limitation set forth in this clause (1); (2) the remaining period of time for exercise of such stock options under the option agreement(s) pursuant to which such stock options were granted; or (3) such period of time (which period of time may end as early as the consummation of a Change in Control) as the Board of Directors may determine in connection with or in contemplation of a Change in Control in the exercise of its discretion under the applicable stock option plans, with respect to which the Board of Directors has the discretion to, among other things, require the surrender of stock options (which surrender may be in exchange for a cash payment, if applicable) and to cancel such stock options upon the consummation of a Change in Control as further described in the applicable stock option plans. If a Covered Individual’s employment becomes subject to an Involuntary Termination after his stock options have vested under this Section 4.12, the stock option exercise provisions of Subsection 3.1(c) shall apply upon such Covered Individual becoming subject to an Involuntary Termination.”

3. Except as modified herein, the Second Supplement shall remain in full force and effect.

EXECUTED this 31st day of October, 2005.