<PAGE>
                                                                    Exhibit 10.1

                                 FIRST AMENDMENT

          FIRST AMENDMENT, dated as of November 3, 2005 (this "Amendment"), to
the Credit Agreement, dated as of November 9, 2004 (the "Credit Agreement"),
among HCA INC., a Delaware corporation (the "Borrower"), the several banks and
other financial institutions from time to time parties hereto (the "Banks"),
BANK OF AMERICA, N.A., as Documentation Agent and Co-Arranger, CITICORP NORTH
AMERICA, INC., DEUTSCHE BANK SECURITIES INC., MIZUHO CORPORATE BANK, LTD. and
WACHOVIA BANK, NATIONAL ASSOCIATION, as Syndication Agents and Co-Arrangers, THE
BANK OF NOVA SCOTIA, MERRILL LYNCH & CO., MERRILL LYNCH, PIERCE, FENNER & SMITH
INCORPORATED and SUNTRUST BANK, as Senior Managing Agents, THE BANK OF NEW YORK,
KEY BANK and CALYON NEW YORK BRANCH, as Managing Agents, AMSOUTH BANK, FIFTH
THIRD BANK, N.A., THE NORTHERN TRUST COMPANY, SUMITOMO BANK, US BANK, NA and
UNION PLANTERS BANK, N.A, as Co-Agents, J.P. MORGAN SECURITIES INC., as Sole
Advisor, Lead Arranger and Bookrunner, and JPMORGAN CHASE BANK, N.A. (formerly
known as JPMORGAN CHASE BANK), as administrative agent (in such capacity, the
"Agent").

                                   WITNESSETH:

          WHEREAS, the Borrower has requested that the Credit Agreement be
amended as set forth herein; and

          WHEREAS, the Required Banks have agreed to such amendment and have
authorized the Agent to execute this Amendment in accordance with the terms and
conditions set forth herein;

          NOW THEREFORE, in consideration of the premises herein contained and
for other good and valuable consideration, the receipt of which is hereby
acknowledged, the parties hereto hereby agree as follows:

          1. Defined Terms. Unless otherwise defined herein, terms defined in
the Credit Agreement and used herein shall have the meanings given to them in
the Credit Agreement.

          2. Amendment to Section 6.6. Section 6.6 of the Credit Agreement is
hereby amended by deleting the section in its entirety and inserting in lieu
thereof the following:

          6.6 Ratio of Consolidated Total Debt to Consolidated Total
          Capitalization. The Company and its Subsidiaries will not at any time
          have outstanding Consolidated Total Debt in an amount in excess of (i)
          75% of Consolidated Total Capitalization from the Closing Date through
          September 30, 2005, (ii) 80% of Consolidated Total Capitalization from
          October 1, 2005 through December 30, 2006, (iii) 75% of Consolidated
          Total Capitalization
<PAGE>
          from December 31, 2006 through December 30, 2007, (iv) 70% of
          Consolidated Total Capitalization from December 31, 2007 through
          December 30, 2008 and (v) 65% of Consolidated Total Capitalization
          from December 31, 2008 and thereafter.

          3. Effective Date; Conditions Precedent. This Amendment shall become
effective on November 3, 2005 (the "Effective Date") subject to the compliance
by the Borrower with its agreements herein contained and to the satisfaction on
or before the Effective Date of the following further conditions:

             (a) Loan Documents. The Agent shall have received counterparts
hereof duly executed by the Borrower, the Agent and the Required Banks.

             (b) Fees. The Agent shall have received, for the account of each
Bank which executes and delivers this Amendment on or prior to 5:00 p.m. New
York City time on October 27, 2005, an amendment fee in an amount equal to 3
basis points on such Bank's Commitment as in effect prior to the Effective Date,
payable in immediately available funds on or before the Effective Date.

          4. Representations and Warranties. The Borrower hereby represents and
warrants on the date hereof that (i) all of the Borrower's representations and
warranties contained in the Credit Agreement are true and correct in all
material respects as of the date hereof (except for representations and
warranties made as of a specified date, which shall be true and correct as of
such date) and (ii) no Default shall have occurred (except a Default which shall
have been waived in writing or which shall have been cured) and no Default shall
exist before and after giving effect to this Amendment.

          5. Continuing Effect of Credit Agreement. This Amendment shall not be
construed as a waiver of or consent to any further or future action on the part
of the Borrower that would require a waiver or consent by the Agent and/or the
Banks. Except as expressly amended hereby, the Credit Agreement shall continue
to be and shall remain in full force and effect in accordance with its terms.

          6. Counterparts. This Amendment may be executed by one or more of the
parties hereto on any number of separate counterparts, and all of said
counterparts taken together shall be deemed to constitute one and the same
instrument. Delivery of an executed signature page of this Amendment by
facsimile transmission shall be effective as delivery of a manually executed
counterpart hereof.

          7. GOVERNING LAW. THIS AMENDMENT SHALL BE GOVERNED BY, AND CONSTRUED
AND INTERPRETED IN ACCORDANCE WITH, THE LAWS OF THE STATE OF NEW YORK.

          8. Expenses. The Borrower agrees to pay or reimburse the Agent for all
of its reasonable out-of-pocket costs and expenses incurred in connection with
the preparation, negotiation and execution of this Amendment, including, without
limitation, the reasonable fees and disbursements of counsel to the Agent.
<PAGE>
          IN WITNESS WHEREOF, the parties hereto have caused this Amendment to
be executed and delivered by their duly authorized officers as of the date first
written above.

                              HCA INC.


                              By: /s/ David G. Anderson
                                  ----------------------------------------------
                              Name: David G. Anderson
                                    --------------------------------------------
                              Title: Senior Vice President-Finance and Treasurer
                                     -------------------------------------------


                              JPMORGAN CHASE BANK, N.A., as Agent and
                              as a Bank


                              By: /s/ Dawn Lee Lum
                                  ----------------------------------------------
                              Name: Dawn Lee Lum
                                    --------------------------------------------
                              Title: Vice President
                                     -------------------------------------------
<PAGE>
                                        Am South Bank
                                        [NAME OF LENDER]

                                        By: Bill Berrell
                                            ------------------------------------
                                        Name:  Bill Berrell
                                        Title: Vice President

<PAGE>
                                        BABSON CLO LTD. 2005-II
                                        By: Babson Capital Management LLC as
                                        Collateral Manager

                                        By: /s/ Glenn P Duffy
                                            ----------------------------

                                        Name: Glenn P Duffy, CFA
                                              --------------------------

                                        Title: Managing Director
                                               -------------------------
<PAGE>

                                        Bank of America, N.A.



                                        By: /s/ Kevin Wagley
                                            ----------------------------

                                        Name: Kevin Wagley
                                              --------------------------

                                        Title: Senior Vice President
                                               -------------------------
<PAGE>
                                         Bank of Communications, New York Branch


                                         By:  /s/ Yuning Liu
                                              --------------------------------
                                              Name:  Yuning Liu
                                              Title: Deputy General Manager




<PAGE>



                                         The Bank of Nova Scotia



                                         By:  /s/ Dana C. Maloney
                                              ----------------------------
                                              Dana C. Maloney
                                              Managing Director



<PAGE>




                                         Bank of Taiwan, New York Agency


                                         By:  /s/ Eunice S.J. Yeh
                                              ---------------------------
                                              Name: Eunice S.J. Yeh
                                              Title:  SVP & GM



<PAGE>



                               [NAME OF LENDER]:  Monument Park CDO Ltd.
                                                  Blackstone Debt Advisors L.P.
                                                  As Collateral Manager


                               By:  /s/ DEAN T CRIARES
                                    -----------------------------
                                    Name:  DEAN T CRIARES
                                    Title:   Managing Director


























<PAGE>





                                                      BNP PARIBAS

                                                      By: /s/ William Duke
                                                          ---------------------
                                                          Name: William Duke
                                                          Title: Director






<PAGE>



                                                 The Bank of New York

                                                 By: /s/ Christopher T. Kordes
                                                     -------------------------
                                                     Name: Christopher T. Kordes
                                                     Title: Vice President


<PAGE>

                                                Carolina First Bank

                                                By: /s/ Charles D. Chamberlain
                                                    --------------------------
                                                    Charles D. Chamberlain
                                                    Executive Vice President
<PAGE>



                                             CITICORP NORTH AMERICA, INC.

                                             By: /s/ Allen Fisher
                                                 ----------------------
                                             Name: Allen Fisher
                                             Title: Director
<PAGE>


                                            CALYON New York Branch, as a Lender


                                            By: /s/ Charles Heidsieck
                                               ------------------------------
                                            Name: Charles Heidsieck
                                            Title: Managing Director



                                            By: /s/ Thomas Randolph
                                               ------------------------------
                                            Name: Thomas Randolph
                                            Title: Director

<PAGE>


                                             Deutsche Bank AG New York Branch



                                             By: /s/ Frederick W. Laird
                                                 -------------------------------
                                                 Name: Frederick W. Laird
                                                 Title: Managing Director




                                             By: /s/ Ming K. Chu
                                                 -------------------------------
                                                 Name: Ming K. Chu
                                                 Title: Vice President
<PAGE>

                              [NAME OF LENDER]
                              Dresdner Bank AG New York &
                              Grand Cayman Branches

                              By: /s/ Daniel Conlon         /s/ Janet Wolff
                                  -------------------       -------------------
                                  Name: Daniel Conlon       Name: Janet Wolff
                                  Title: Director           Title: Director

<PAGE>
                                             Fifth Third Bank
                                             [NAME OF LENDER]

                                             By: /s/ Sandy Nawrick
                                                ----------------------------
                                                Name: Sandy Nawrick
                                                Title:
<PAGE>


                                               First Commercial Bank New York
                                               Agency


                                               By: /s/ Bruce M.J. Ju
                                                   ----------------------
                                                   Name: Bruce M.J. Ju
                                                   Title: VP & General Manager
<PAGE>
                                             Hua Nan Commercial Bank LTD, New
                                             York Agency


                                             By: /s/ Daniel Huang
                                                 --------------------------
                                             Name: Daniel Huang
                                             Title: General Manager
<PAGE>



                                   Katonah VII, Ltd.


                                   By: /s/ Daniel Gilligan
                                      -------------------------------------
                                      Name:  Daniel Gilligan
                                      Title: Authorized Officer
                                             Katonah Debt Advisors, L.L.C.
                                             As Manager

<PAGE>

                                   KEYBANK NATIONAL ASSOCIATION


                                   By: /s/ J.T. Taylor
                                      -------------------------------------
                                      Name:  J.T. Taylor
                                      Title: Senior Vice President
<PAGE>





                                   MERRILL LYNCH BANK USA


                                   By: /s/ David Millett
                                      -------------------------------------
                                   Name:  David Millett
                                   Title: Vice President

<PAGE>





                                   MERRILL LYNCH CAPITAL CORP.


                                   By: /s/ Michael E. O'Brien
                                      -------------------------------------
                                      Name:  Michael E. O'Brien
                                      Title: Vice President

<PAGE>





                                   MIZUHO CORPORATE BANK, LTD.


                                   By: /s/ Takahiko Ueda
                                      -------------------------------------
                                   Name:  Takahiko Ueda
                                   Title: Deputy General Manager

<PAGE>





                                   NATIONAL CITY BANK OF KENTUCKY


                                   By: /s/ Erica Dowd
                                      -------------------------------------
                                      Name:  Erica Dowd
                                      Title: AVP

<PAGE>





                                   THE NORTHERN TRUST COMPANY


                                   By: /s/ Preeti Sullivan
                                      -------------------------------------
                                      Name:  Preeti Sullivan
                                      Title: Vice President

<PAGE>






                                   [NAME OF LENDER]


                                   By: /s/ John Randolph Watkins
                                      -------------------------------------
                                      Name:  John Randolph Watkins
                                      Title: Executive Director



<PAGE>





                                   Scotiabanc Inc.


                                   By: /s/ William E. Zarrett
                                      -------------------------------------
                                   William E. Zarrett
                                   Managing Director

<PAGE>

                                     STATE BANK OF INDIA,
                                     NASSAU

                                     By: KARAMJIT SINGH
                                         --------------------------
                                         Name:  KARAMJIT SINGH
                                         Title: CHIEF EXECUTIVE OFFICER (SEAL)
<PAGE>

                                        Sumitomo Mitsui Banking Corporation
                                        [NAME OF LENDER]

                                        By: /s/ David A. Buck
                                            ------------------------------

                                            Name: David A. Buck
                                            Title: Senior Vice President
<PAGE>



                                             [NAME OF LENDER] Sun Trust Bank

                                             By: /s/ Mark D. Mattson
                                                ---------------------------
                                                Name:  Mark D. Mattson
                                                Title: Managing Director
<PAGE>


                                             REGIONS BANK

                                             By: /s/ Craig Gardella
                                                ---------------------------
                                                Name:  CRAIG E. GARDELLA
                                                Title: SENIOR VICE PRESIDENT
<PAGE>
                                   [NAME OF LENDER]
                                   U.S. Bank, N.A.


                                   By: /s/ S.W. CHOPPIN
                                       ---------------------------
                                       Name:  S. W. CHOPPIN
                                       Title:  S.V.P.






<PAGE>





                                   Wachovia Bank, National Association



                                   By:  /s/ Jeanette A. Griffin
                                        ------------------------------------
                                        Name:  Jeanette A. Griffin
                                        Title: Director