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


November 19, 2004

063718.0102


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 up to 59,500,000 shares
of common stock, par value $2.50 per share, of the Company (the "Shares") that
may be sold by the selling stockholder 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 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, 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.

         On the basis of the foregoing, and subject to the qualifications and
limitations hereinafter set forth, we are of the opinion that the Shares have
been duly authorized and, when issued to the selling stockholder as described in
the Registration Statement, registered and delivered, the Shares will be validly
issued, fully paid and non-assessable.


BAKER BOTTS L.L.P.
Halliburton Company                    2                       November 19, 2004


         The opinion set forth above is limited in all respects to (1) 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 (2) 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