EXHIBIT 5.1


                        (BAKER BOTTS L.L.P. LETTERHEAD)



November 19, 2004

063718.0509


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 $500,000,000 aggregate
principal amount of Senior Notes Due 2007 (the "Notes") issued pursuant to an
Indenture (the "Indenture") dated as of October 17, 2003 between the Company and
JPMorgan Chase Bank, as trustee (the "Trustee"), as supplemented by the Third
Supplemental Indenture, dated as of January 26, 2004, 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. 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, (ii) the Notes have been
duly authenticated by the Trustee and (iii) the Indenture has been validly
qualified under the Trust Indenture Act of 1939.


BAKER BOTTS L.L.P.

Halliburton Company                          2                 November 19, 2004


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

                  The opinion set forth above is limited in all respects to (1)
matters of the laws of the State of New York, (2) the General Corporation Law of
the State of Delaware, which includes the statutory provisions and also all
applicable provisions of the Delaware Constitution and reported judicial
decisions interpreting these laws, and (3) 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.



DWT/JDS