EXHIBIT 24.1

POWER OF ATTORNEY

KNOW ALL PERSONS BY THESE PRESENTS:

     WHEREAS, Unocal Capital Trust II, a Delaware statutory trust (the “Trust”) contemplates filing with the Securities and Exchange Commission (the “SEC”) at Washington, D.C., under the Securities Act of 1933, as amended, and the regulations promulgated thereunder, post-effective amendments to Registration Statements previously filed on Form S-3 for the purpose of withdrawing any unsold securities from registration with the SEC (the “Post-Effective Amendments”); and

     WHEREAS, the Trust further contemplates filing with the SEC at Washington, D.C., under the Securities Act of 1933, as amended, and the regulations promulgated thereunder, a Form 15 for the purpose of suspending the Trust’s reporting obligations under the Securities Exchange Act of 1934, as amended (the “Form 15”); and

     WHEREAS, the undersigned is a trustee of the Trust;

     NOW, THEREFORE, effective as of the effective time of the merger of Unocal Corporation (“Unocal”), with and into Blue Merger Sub Inc. (“Merger Sub”), a wholly-owned subsidiary of Chevron Corporation (“Chevron”), pursuant to the Agreement and Plan of Merger, dated April 4, 2005, as amended, by and among Chevron, Unocal and Merger Sub, the undersigned hereby constitutes and appoints KIMBERLEY C. SCHAFER, LYDIA I. BEEBE, CHRISTOPHER A. BUTNER, PATRICIA LOVETT TAI, or any one of them, his or her attorneys-in-fact and agents, with full power of substitution and re-substitution, for such person and in his or her name, place and stead, in any and all capacities, to sign the aforementioned Post-Effective Amendments and Form 15 (and any and all other filings with the SEC necessary to cause the termination of such Registration Statements and the withdrawal of the Trust’s registered securities) and to file the same, with all exhibits thereto, and other documents in connection therewith, with the SEC, granting unto said attorneys-in-fact and agents full power and authority to do and perform each and every act and thing requisite and necessary to be done in and about the premises, as fully as to all intents and purposes he or she might or could do in person, hereby ratifying and confirming all that said attorneys-in-fact and agents, or their substitutes, may lawfully do and cause to be done by virtue hereof.

     IN WITNESS WHEREOF, the undersigned has hereunto set his or her hand this 8th day of August, 2005.

By:	/s/ DARRELL D. CHESSUM
	Darrell D. Chessum