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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(Print or Type Responses)

1. Name and Address of Reporting Person * GAUT C CHRISTOPHER   2. Issuer Name and Ticker or Trading Symbol HALLIBURTON CO [HAL] 5. Relationship of Reporting Person(s) to Issuer (Check all applicable) _____ Director _____ 10% Owner __X__ Officer (give title below) _____ Other (specify below) Exec VP and CFO (Last) (First) (Middle) 1401 MCKINNEY STREET, SUITE 2400 3. Date of Earliest Transaction (Month/Day/Year) 05/13/2005 (Street) HOUSTON, TX 77010 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 05/13/2005   D   1,050 (1) D $ 44.08 77,818 (2) D

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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

Option to Buy Common Stock

$ 38.61

12/02/2004

12/02/2014

Common Stock

16,500

16,500

D

Option to Buy Common Stock

$ 26.03

01/02/2004

01/02/2014

Common Stock

32,940

32,940

D

Option to Buy Common Stock

$ 20.5

03/03/2004

03/03/2013

Common Stock

100,000

100,000

D

Reporting Owners

Reporting Owner Name / Address	Relationships
	Director	10% Owner	Officer	Other
GAUT C CHRISTOPHER 1401 MCKINNEY STREET SUITE 2400 HOUSTON, TX 77010			Exec VP and CFO

Signatures

Margaret E. Carriere, by Power of Attorney		05/13/2005
**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)	Shares transferred to Halliburton Company for payment for Federal Income Tax withholding obligations on lapse of restrictions on shares issued under the 1993 Stock and Incentive Plan. Said Plan permits Reporting Person to satisfy withholding tax obligation by transferring unrestricted shares to the Issuer.
(2)	Includes 908 shares acquired under the Halliburton Company Employees Stock Purchase Plan through January 2005.

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