Exhibit 24.9

POWER OF ATTORNEY

WHEREAS, Chevron Corporation, a Delaware corporation (the “Corporation”), contemplates filing with the Securities and Exchange Commission in Washington, D.C., under the provisions of the Securities Act of 1933, as amended, and the regulations promulgated thereunder, a Registration Statement on Form S-8 for the Long-Term Incentive Plan of Chevron Corporation and a Registration Statement on Form S-8 for the Chevron Corporation Deferred Compensation Plan For Management Employees II (and any and all amendments thereto, including post-effective amendments);

WHEREAS, the undersigned is an officer or director, or both, of the Corporation;

NOW, THEREFORE, the undersigned hereby constitutes and appoints LYDIA I. BEEBE, CHRISTOPHER A. BUTNER, PATRICIA L. TAI, WALKER C. TAYLOR, or any of them, his or her attorneys-in-fact and agents, with full power of substitution and resubstitution, for such person and in his or her name, place and stead, in any and all capacities, to sign the aforementioned Registration Statement (and any and all amendments thereto, including post-effective amendments) and to file the same, with all exhibits thereto, and other documents in connection therewith, with the Securities and Exchange Commission, 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 31st day of July, 2013.

/s/ Carl Ware