EXHIBIT 5.1


BAKER BOTTS L.L.P.                            ONE SHELL PLAZA        AUSTIN
                                              910 LOUISIANA          BAKU
                                              HOUSTON, TEXAS         DALLAS
                                              77002-4995             HOUSTON
                                              713.229.1234           LONDON
                                              FAX 713.229.1522       MOSCOW
                                                                     NEW YORK
                                                                     RIYADH
                                                                     WASHINGTON


February 6, 2004

063718.0176


Halliburton Company
1401 McKinney, Suite 2400
Houston, Texas 77010

Ladies and Gentlemen:

                  As set forth in the Registration Statement on Form S-3 (the
"Registration Statement") filed by Halliburton Company, a Delaware corporation
(the "Company"), with the Securities and Exchange Commission (the "Commission")
under the Securities Act of 1933, as amended (the "Act"), relating to the
registration under the Act of the offering and sale of (i) $1,200,000,000
aggregate principal amount of 3 1/8% Convertible Senior Notes Due 2023 (the
"Notes") issued pursuant to an Indenture (the "Indenture") dated as of June 30,
2003 between the Company and JPMorgan Chase Bank, as trustee (the "Trustee"),
and (ii) such indeterminate number of shares of common stock, par value $2.50
per share, of the Company issuable upon the conversion of the Notes (the
"Conversion Shares"), in each case that may be sold by the selling
securityholders referred to in the Registration Statement from time to time
pursuant to Rule 415 under the Act, we are passing upon certain legal matters
for the Company in connection with the Notes and the Conversion Shares. At your
request, this opinion is being furnished to you for filing as Exhibit 5.1 to the
Registration Statement.

                  In our capacity as your counsel in connection with the matters
referred to above, we have examined originals, or copies certified or otherwise
identified, of the Restated Certificate of Incorporation and Bylaws of the
Company, each as amended to date, the Indenture, the Notes, corporate records of
the Company, including minute books of the Company as furnished to us by the
Company, certificates of public officials and of representatives of the Company,
statutes and other instruments and documents as a basis for the opinions
hereinafter expressed. In giving such opinions, we have relied upon certificates
of officers of the Company and of public officials with respect to the accuracy
of the material factual matters contained in such certificates. In giving the
opinions below, we have assumed that the signatures on all documents examined by
us are genuine, that all documents submitted to us as originals are accurate and
complete, that all documents submitted to us as copies are true and correct
copies of the originals thereof and that all information submitted to us was
accurate and complete. In addition, we have assumed that (i) the Indenture has
been duly authorized, executed and delivered by the Trustee and constitutes the
legal, valid and binding obligation of the Trustee and (ii) the Notes have been
duly authenticated by the Trustee.




BAKER BOTTS L.L.P.

Halliburton Company                     2                       February 6, 2004


                  On the basis of the foregoing, and subject to the
qualifications and limitations hereinafter set forth, we are of the opinion
that:

                  1. The Notes constitute legal, valid and binding obligations
         of the Company, enforceable against the Company, except as the
         enforceability thereof is subject to the effect of (i) bankruptcy,
         insolvency, reorganization, moratorium, fraudulent transfer or
         conveyance or other laws relating to or affecting creditors' rights
         generally and (ii) general principles of equity (regardless of whether
         such enforceability is considered in a proceeding in equity or at law).

                  2. The Conversion Shares have been duly authorized and
         reserved for issuance and, when certificates representing the
         Conversion Shares have been duly executed, countersigned, registered
         and delivered upon conversion of the Notes in accordance with the terms
         of the Notes and the Indenture, the Conversion Shares will be validly
         issued, fully paid and non-assessable.

                  The opinions set forth above are limited in all respects to
matters of the laws of the State of New York, the General Corporation Law of the
State of Delaware and applicable federal law. We hereby consent to the filing of
this opinion with the Commission as Exhibit 5.1 to the Registration Statement.
We also consent to the reference to our Firm under the heading "Legal Matters"
in the prospectus forming a part of the Registration Statement. In giving such
consent, we do not hereby admit that we are in the category of persons whose
consent is required under Section 7 of the Act or the rules and regulations of
the Commission thereunder.


                                        Very truly yours,

                                        BAKER BOTTS L.L.P.