FORM 4 Check this box if no longer subject to Section 16. Form 4 or Form 5 obligations may continue. See Instruction 1(b).

UNITED STATES SECURITIES AND EXCHANGE COMMISSION Washington, D.C. 20549 STATEMENT OF CHANGES IN BENEFICIAL OWNERSHIP OF SECURITIES Filed pursuant to Section 16(a) of the Securities Exchange Act of 1934, Section 17(a) of the Public Utility Holding Company Act of 1935 or Section 30(h) of the Investment Company Act of 1940

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1. Name and Address of Reporting Person * HERNANDEZ ENRIQUE JR   2. Issuer Name and Ticker or Trading Symbol CHEVRON CORP [CVX] 5. Relationship of Reporting Person(s) to Issuer (Check all applicable) __X__ Director _____ 10% Owner _____ Officer (give title below) _____ Other (specify below) (Last) (First) (Middle) INTER-CON SECURITY SYSTEMS, INC., 210 SOUTH DE LACEY AVENUE 3. Date of Earliest Transaction (Month/Day/Year) 05/27/2009 (Street) PASADENA, CA 91105 4. If Amendment, Date Original Filed(Month/Day/Year) 6. Individual or Joint/Group Filing(Check Applicable Line) _X_ Form filed by One Reporting Person ___ Form filed by More than One Reporting Person (City) (State) (Zip) Table I - Non-Derivative Securities Acquired, Disposed of, or Beneficially Owned

1.Title of Security (Instr. 3) 2. Transaction Date (Month/Day/Year) 2A. Deemed Execution Date, if any (Month/Day/Year) 3. Transaction Code (Instr. 8) 4. Securities Acquired (A) or Disposed of (D) (Instr. 3, 4 and 5) 5. Amount of Securities Beneficially Owned Following Reported Transaction(s) (Instr. 3 and 4) 6. Ownership Form: Direct (D) or Indirect (I) (Instr. 4) 7. Nature of Indirect Beneficial Ownership (Instr. 4) Code V Amount (A) or (D) Price Common Stock 05/27/2009   A   2,802 (1) A $ 0 3,834 (2) D   Common Stock               1,220 I by Hernandez Family Trust

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Table II - Derivative Securities Acquired, Disposed of, or Beneficially Owned
(e.g., puts, calls, warrants, options, convertible securities)

1. Title of Derivative Security (Instr. 3)

2. Conversion or Exercise Price of Derivative Security

3. Transaction Date (Month/Day/Year)

3A. Deemed Execution Date, if any (Month/Day/Year)

4. Transaction Code (Instr. 8)

5. Number of Derivative Securities Acquired (A) or Disposed of (D) (Instr. 3, 4, and 5)

6. Date Exercisable and Expiration Date (Month/Day/Year)

7. Title and Amount of Underlying Securities (Instr. 3 and 4)

8. Price of Derivative Security (Instr. 5)

9. Number of Derivative Securities Beneficially Owned Following Reported Transaction(s) (Instr. 4)

10. Ownership Form of Derivative Security: Direct (D) or Indirect (I) (Instr. 4)

11. Nature of Indirect Beneficial Ownership (Instr. 4)

Code

V

(A)

(D)

Date Exercisable

Expiration Date

Title

Amount or Number of Shares

Non-Qualified Stock Option (Right to Buy) (3)

$ 64.57

05/27/2009

A

7,923

05/27/2010(4)

05/27/2019

Common Stock

7,923

$ 0

7,923

D

Reporting Owners

Reporting Owner Name / Address	Relationships
	Director	10% Owner	Officer	Other
HERNANDEZ ENRIQUE JR INTER-CON SECURITY SYSTEMS, INC. 210 SOUTH DE LACEY AVENUE PASADENA, CA 91105	X

Signatures

Christopher A. Butner on behalf of Enrique Hernandez, Jr.		05/29/2009
**Signature of Reporting Person		Date

Explanation of Responses:

*	If the form is filed by more than one reporting person, see Instruction 4(b)(v).
**	Intentional misstatements or omissions of facts constitute Federal Criminal Violations. See 18 U.S.C. 1001 and 15 U.S.C. 78ff(a).
(1)	This number represents stock units issued under the Non-Employee Directors' Equity Compensation and Deferral Plan.
(2)	This number includes the acquisition of dividend equivalent accruals on stock units (11 shares) issued under the Non-Employee Directors' Equity Compensation and Deferral Plan.
(3)	Stock option granted in lieu of the annual cash retainer at the Director's election.
(4)	The option vests as follows: 50 percent on November 27, 2009 and the remaining 50 percent on the earlier of the last day of the Annual Compensation Cycle to which the grant relates or May 27, 2010.

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