SEC Form 4

FORM 4		UNITED STATES SECURITIES AND EXCHANGE COMMISSION Washington, D.C. 20549 STATEMENT OF CHANGES IN BENEFICIAL OWNERSHIP Filed pursuant to Section 16(a) of the Securities Exchange Act of 1934 or Section 30(h) of the Investment Company Act of 1940	OMB APPROVAL OMB Number: 3235-0287 Estimated average burden hours per response: 0.5
	Check this box if no longer subject to Section 16. Form 4 or Form 5 obligations may continue. See Instruction 1(b).

1. Name and Address of Reporting Person* GIBSON JOHN W JR (Last) (First) (Middle) 10200 BELLAIRE BLVD. (Street) HOUSTON TX 77072 (City) (State) (Zip)	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) Pres & CEO Energy Services Grp
	3. Date of Earliest Transaction (Month/Day/Year) 05/20/2004
	4. If Amendment, Date of 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

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	05/20/2004		D		898(1)	D	$31.96	157,483	D
Common Stock	05/20/2004		D		549(1)	D	$30.04	156,934	D

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 Securities Underlying Derivative Security (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: 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	$26.03							01/02/2004	01/02/2014	Common Stock	32,940		32,940	D
Option to Buy Common Stock	$26.875							10/04/1996	10/04/2006	Common Stock	34,000		34,000	D
Option to Buy Common Stock	$29.5625							12/04/1996	12/04/2006	Common Stock	24,000		24,000	D
Option to Buy Common Stock	$54.5							12/03/1997	12/03/2007	Common Stock	12,000		12,000	D
Option to Buy Common Stock	$28.125							12/02/1998	12/02/2008	Common Stock	12,000		12,000	D
Option to Buy Common Stock	$39.5							12/02/1999	12/02/2009	Common Stock	28,500		28,500	D
Option to Buy Common Stock	$34.75							12/06/2000	12/06/2010	Common Stock	39,000		39,000	D
Option to Buy Common Stock	$31.55							07/19/2001	07/19/2011	Common Stock	21,938		21,938	D
Option to Buy Common Stock	$49.9375							05/15/1999	05/15/2009	Common Stock	10,000		10,000	D

Explanation of Responses:

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.

Remarks:

	Michael A. Weberpal, by Power of Attorney	05/21/2004
	** Signature of Reporting Person	Date
Reminder: Report on a separate line for each class of securities beneficially owned directly or indirectly.
* 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).
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