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 * O REILLY DAVID J   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 __X__ Officer (give title below) _____ Other (specify below) Chairman of the Board and CEO (Last) (First) (Middle) 6001 BOLLINGER CANYON ROAD 3. Date of Earliest Transaction (Month/Day/Year) 05/03/2006 (Street) SAN RAMON, CA 94583 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 05/03/2006   M   70,000 (1) A $ 40.4688 94,994 (2) D   Common Stock 05/03/2006   M   117,200 A $ 39.5625 212,194 D   Common Stock 05/03/2006   M   300,000 A $ 44.9375 512,194 D   Common Stock 05/03/2006   S   1,000 D $ 62.69 511,194 D   Common Stock 05/03/2006   S   7,000 D $ 62.68 504,194 D   Common Stock 05/03/2006   S   8,800 D $ 62.67 495,394 D   Common Stock 05/03/2006   S   1,100 D $ 62.66 494,294 D   Common Stock 05/03/2006   S   1,000 D $ 62.65 493,294 D   Common Stock 05/03/2006   S   2,200 D $ 62.55 491,094 D   Common Stock 05/03/2006   S   1,000 D $ 62.54 490,094 D   Common Stock 05/03/2006   S   29,600 D $ 62.53 460,494 D   Common Stock 05/03/2006   S   1,300 D $ 62.5 459,194 D   Common Stock 05/03/2006   S   800 D $ 62.49 458,394 D   Common Stock 05/03/2006   S   16,200 D $ 62.48 442,194 D   Common Stock 05/03/2006   S   16,300 D $ 62.48 425,894 D   Common Stock 05/03/2006   S   2,300 D $ 62.47 423,594 D   Common Stock 05/03/2006   S   2,100 D $ 62.46 421,494 D   Common Stock 05/03/2006   S   5,300 D $ 62.45 416,194 D   Common Stock 05/03/2006   S   1,700 D $ 62.44 414,494 D   Common Stock 05/03/2006   S   2,700 D $ 62.43 411,794 D   Common Stock 05/03/2006   S   4,000 D $ 62.42 407,794 D   Common Stock 05/03/2006   S   2,000 D $ 62.41 405,794 D   Common Stock 05/03/2006   S   2,700 D $ 62.4 403,094 D   Common Stock 05/03/2006   S   700 D $ 62.39 402,394 D   Common Stock 05/03/2006   S   300 D $ 62.38 402,094 D   Common Stock               65,522 (3) I by 401(k) plan

Reminder: Report on a separate line for each class of securities beneficially owned directly or indirectly.
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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)

$ 40.4688 (4)

05/03/2006

M

70,000 (4)

10/29/1998

10/29/2007

Common Stock

70,000 (4)

$ 0

0

D

Non-Qualified Stock Option (Right to Buy)

$ 39.5625 (4)

05/03/2006

M

117,200 (4)

10/27/1999

10/27/2008

Common Stock

117,200 (4)

$ 0

0

D

Non-Qualified Stock Option (Right to Buy)

$ 44.9375 (4)

05/03/2006

M

300,000 (4)

10/27/2000

10/27/2009

Common Stock

300,000 (4)

$ 0

0

D

Reporting Owners

Reporting Owner Name / Address	Relationships
	Director	10% Owner	Officer	Other
O REILLY DAVID J 6001 BOLLINGER CANYON ROAD SAN RAMON, CA 94583	X		Chairman of the Board and CEO

Signatures

Christopher A. Butner on behalf of David J. O'Reilly		05/05/2006
**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)	The Form 4 is one of three being filed to report transactions occurring on May 3, 2006.
(2)	This number includes the acquisition of 12,497 shares from the September 10, 2004, 2-for-1 stock split of Chevron Corporation common stock.
(3)	Between August 7, 2004 and May 2, 2006, the reporting person acquired 35,031 shares of Chevron Corporation common stock under the Chevron Employee Savings Investment Plan, a 401(k) plan. This number includes the September 10, 2004, 2-for-1 stock split.
(4)	The option exercise price and number of shares are adjusted for the September 10, 2004, 2-for-1 stock split of Chevron Corporation common stock.

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