<PAGE>

                                                                    Exhibit 10.1

                     AMENDMENT TO THE OPERATING AGREEMENT OF
                    ST. LANDRY EXTENDED CARE HOSPITAL, L.L.C.

     This Amendment to the Operating Agreement of St. Landry Extended Care
Hospital, LLC, (dated April 15, 2004 and hereinafter referred to as the
"Original Operating Agreement") shall be effective as of November 9, 2005
("Effective Date").

                                   BACKGROUND

     The Company's members desire to amend the Original Operating Agreement to
reflect that as a result of its merger with LHC Group, LLC, LHC Group, Inc. is
now serving as Manager of St. Landry Extended Care Hospital, LLC ("the
Company").

     The Company's Members desire to amend the Original Operating Agreement's
calculation of the Company and Manager's Earnings Before Interest, Taxes,
Depreciation and Amortization valuation "EBITDA" as it relates to the conversion
options of the members.

     Accordingly, the Company's Members hereby amend the Original Operating
Agreement as of the Effective Date as follows:

1. Amendment to Section 4.1(a). Section 4.1(a) of the Original Operating
Agreement is hereby amended to provide for LHC Group, Inc.'s status as manager
of the Company. Hereafter section 4.1(a) shall read as follows:

4.1  MANAGERS

     (a)  THE BUSINESS OF THE COMPANY SHALL BE MANAGED BY ONE OR MORE MANAGERS,
          WHO MAY, BUT NEED NOT, BE MEMBERS, AND WHO SHALL BE A MANDATORY OF THE
          COMPANY FOR ALL MATTERS IN THE ORDINARY COURSE OF BUSINESS. LHC GROUP,
          INC. SHALL BE THE MANAGER OF THE COMPANY, AND APPEARS HEREIN TO ACCEPT
          SAID APPOINTMENT. TO THE EXTENT AUTHORIZED BY THIS AGREEMENT, THE
          MANAGER SHALL HAVE FULL, EXCLUSIVE AND COMPLETE DISCRETION, CONTROL,
          POWER, AND AUTHORITY IN THE MANAGEMENT OF THE COMPANY'S AFFAIRS. THE
          MANAGER SHALL HAVE FULL POWER AND AUTHORITY TO UNDERTAKE ANY ACTIVITY
          DESCRIBED IN THIS ARTICLE AND TO EXECUTE AND DELIVER ON BEHALF OF THE
          COMPANY SUCH DOCUMENTS OR INSTRUMENTS WHICH THE MANAGER DEEMS
          APPROPRIATE IN THE CONDUCT OF THE COMPANY'S BUSINESS. NO PERSON, FIRM
          OR CORPORATION DEALING WITH THE COMPANY SHALL BE REQUIRED TO INQUIRE
          INTO THE AUTHORITY OF THE MANAGER TO TAKE ANY ACTION OR MAKE ANY
          DECISION

2.   Amendment to Section 6.15(b). Section 6.15(b) of the Original Operating
     Agreement is hereby amended to provide for the calculation of the Company
     and Manager's EBITDA valuation based upon the previous 12 month period
     financial statements ending prior to the effective date of the exercise of
     the conversion option. Hereafter section 6.15(b) shall read as follows:

                                                   Amendment Operating Agreement
                                                                    Page 1 of 18
                                                                November 4, 2005

<PAGE>

     (b)  IN THE EVENT THAT ANY MEMBER EXERCISES THE CONVERSION OPTION, THE
          MEMBER SHALL HAVE THE RIGHT TO EXCHANGE THE UNITS IN THE COMPANY FOR
          MANAGER UNITS IN ACCORDANCE WITH THE FOLLOWING FORMULA:

               THE NUMBER OF UNITS OF MANAGER DUE EACH EXERCISING MEMBER SHALL
          BE THE PRODUCT OF (I) THE EXERCISING MEMBER'S MEMBERSHIP INTEREST IN
          THE COMPANY; (II) THE TOTAL ISSUED AND OUTSTANDING UNITS OF MANAGER AS
          OF THE DATE OF THE NOTICE AND (III) A FRACTION, THE NUMERATOR OF WHICH
          IS THE COMPANY'S EBITDA AND DENOMINATOR OF WHICH IS MANAGER'S EBITDA.

THE EXERCISING MEMBER'S MEMBERSHIP INTEREST IN THE COMPANY SHALL BE DETERMINED
IN ACCORDANCE WITH SECTION 5.1(B). THE COMPANY'S AND MANAGER'S EBITDA SHALL BE
DETERMINED AS THE EARNINGS BEFORE INTEREST, TAXES AND DEPRECIATION FROM THE
COMPANY'S FINANCIAL STATEMENTS AND MANAGER'S CONSOLIDATED FINANCIAL STATEMENTS
FOR THE TWELVE (12) MONTH PERIOD ENDING ON THE LAST DAY OF THE CALENDAR MONTH
PRIOR TO THE EFFECTIVE DATE OF THE EXERCISE OF THE CONVERSION OPTION.

FOR THE PURPOSES OF ILLUSTRATION, THE FOLLOWING EXAMPLE OF HOW THE NUMBER OF
UNITS TO BE CONVERTED WILL BE CALCULATED IS PROVIDED:

                 EBITDA               ISSUED           MEMBER'S    CONVERTED
               12 MONTHS          PROPORTION UNITS     HOLDINGS      UNITS

COMPANY  $ 1,285,000 = 0.0767  X     8,350,000      X    0.1%   = 640.5 UNITS
         -----------                                              -----------
MANAGER  $ 16,751,000


THE PARTIES UNDERSTAND THAT THE FOREGOING EXAMPLE IS FOR PURPOSES OF
ILLUSTRATION ONLY AND IS NOT INDICATIVE OF CURRENT OR FUTURE OPERATIONS OR
PERFORMANCE OF THE COMPANY.

3. Conforming Amendment to Section 6.16(b). Section 6.16(b) of the Original
Operating Agreement is hereby amended to change the reference to the fiscal year
end EBITDA in the illustrative example to read "12 months" in conformance with
the amended formula in Section 6.15 (b). Hereafter section 6.16(b) shall read as
follows:

     "(b) IN THE EVENT THAT ANY MEMBER EXERCISES THE REDEMPTION OPTION, THE
          MEMBER SHALL HAVE THE RIGHT TO SELL HIS HOLDINGS OF UNITS IN THE
          COMPANY TO MANAGER IN ACCORDANCE WITH THE FOLLOWING FORMULA:

              THE SALES PRICE DUE EACH EXERCISING MEMBER SHALL BE THE PRODUCT OF
          (I) THE EXERCISING MEMBER'S POTENTIAL HOLDINGS OF UNITS IN THE MANAGER
          CALCULATED AS IF THE CONVERSION OPTION SET FORTH IN SECTION 6.15 HAD
          BEEN EXERCISED; AND (II) THE AVERAGE CLOSING PRICE OF MANAGER'S UNITS
          OR SHARES FOR THE 30 DAYS PRECEDING THE DATE OF THE MEMBER'S EXERCISE
          OF THE REDEMPTION OPTION.

     FOR THE PURPOSES OF ILLUSTRATION, THE FOLLOWING EXAMPLE OF HOW THE NUMBER
     OF UNITS TO

                                                   Amendment Operating Agreement
                                                                    Page 2 of 18
                                                                November 4, 2005

<PAGE>

     BE CONVERTED WILL BE CALCULATED IS PROVIDED:

               EBITDA                 ISSUED           MEMBER'S      CONVERTED
              12 MONTHS           PROPORTION UNITS     HOLDINGS       UNITS

COMPANY  $ 1,285,000 = 0.0767  X    8,350,000       X    0.1%    =  640.5 UNITS
         -----------                                                -----------
MANAGER  $ 16,751,000


CONVERSION          30 DAY AVE.        PROCEEDS
OPTION UNITS       CLOSING PRICE

  640.5       X       $28.50      =    $18,254
                                       -------

     THE PARTIES UNDERSTAND THAT THE FOREGOING EXAMPLE IS FOR PURPOSES OF
     ILLUSTRATION ONLY AND IS NOT INDICATIVE OF CURRENT OR FUTURE OPERATIONS OR
     PERFORMANCE OF THE COMPANY."

4.   By executing a copy of this Amendment, each of the members consents to the
     entry of LHC Group, Inc. as Manager of the Company, as well as to the
     revision of the EBITDA valuation as it related to the conversion options of
     the members, and each waives any right that he/she/it may have had under
     the Original Operating Agreement.

                       (Signatures on the Following Pages)

                                                   Amendment Operating Agreement
                                                                    Page 3 of 18
                                                                November 4, 2005

<PAGE>

     IN WITNESS WHEREOF, in multiple originals, the undersigned have executed
this Amendment effective as of the Effective Date of this Amendment.

                                         MEMBERS:

                                         LOUISIANA HEALTH CARE GROUP, LLC

                                         By: LHC Group, Inc, Manager

                                         By: /s/ Keith G. Myers
                                             -----------------------------------
                                             Keith G. Myers, President

                                         MANAGER:

                                         LHC GROUP, INC

                                         By: /s/ Keith G. Myers
                                             -----------------------------------
                                             Keith G. Myers, President

                                                   Amendment Operating Agreement
                                                                    Page 4 of 18
                                                                November 4, 2005

<PAGE>

     IN WITNESS WHEREOF, in multiple originals, the undersigned have executed
this Amendment effective as of the Effective Date of this Amendment.

                                         /s/ Louis Nix
                                         ---------------------------------------
                                         LOUIS NIX

                                                   Amendment Operating Agreement
                                                                    Page 5 of 18
                                                                November 4, 2005

<PAGE>

     IN WITNESS WHEREOF, in multiple originals, the undersigned have executed
this Amendment effective as of the Effective Date of this Amendment.

                                         /s/ Paul E. Miller
                                         ---------------------------------------
                                         PAUL E. MILLER

                                                   Amendment Operating Agreement
                                                                    Page 6 of 18
                                                                November 4, 2005

<PAGE>

     IN WITNESS WHEREOF, in multiple originals, the undersigned have executed
this Amendment effective as of the Effective Date of this Amendment.

                                         /s/ Joseph Bordelon
                                         ---------------------------------------
                                         JOSEPH BORDELON

                                                   Amendment Operating Agreement
                                                                    Page 7 of 18
                                                                November 4, 2005

<PAGE>

     IN WITNESS WHEREOF, in multiple originals, the undersigned have executed
this Amendment effective as of the Effective Date of this Amendment.

                                         /s/ Michael Burnell
                                         ---------------------------------------
                                         MICHAEL BURNELL

                                                   Amendment Operating Agreement
                                                                    Page 8 of 18
                                                                November 4, 2005

<PAGE>

     IN WITNESS WHEREOF, in multiple originals, the undersigned have executed
this Amendment effective as of the Effective Date of this Amendment.

                                         /s/ Jose Santiago
                                         ---------------------------------------
                                         JOSE SANTIAGO

                                                   Amendment Operating Agreement
                                                                    Page 9 of 18
                                                                November 4, 2005

<PAGE>

     IN WITNESS WHEREOF, in multiple originals, the undersigned have executed
this Amendment effective as of the Effective Date of this Amendment.

                                         /s/ Ty Hargroder
                                         ---------------------------------------
                                         TY HARGRODER

                                                   Amendment Operating Agreement
                                                                   Page 10 of 18
                                                                November 4, 2005

<PAGE>

     IN WITNESS WHEREOF, in multiple originals, the undersigned have executed
this Amendment effective as of the Effective Date of this Amendment.

                                         /s/ Calvin White
                                         ---------------------------------------
                                         CALVIN WHITE

                                                   Amendment Operating Agreement
                                                                   Page 11 of 18
                                                                November 4, 2005

<PAGE>

     IN WITNESS WHEREOF, in multiple originals, the undersigned have executed
this Amendment effective as of the Effective Date of this Amendment.

                                         /s/ Richard Harmon
                                         ---------------------------------------
                                         RICHARD HARMON

                                                   Amendment Operating Agreement
                                                                   Page 12 of 18
                                                                November 4, 2005

<PAGE>

     IN WITNESS WHEREOF, in multiple originals, the undersigned have executed
this Amendment effective as of the Effective Date of this Amendment.

                                         /s/ Gary Blanchard
                                         ---------------------------------------
                                         GARY BLANCHARD

                                                   Amendment Operating Agreement
                                                                   Page 13 of 18
                                                                November 4, 2005

<PAGE>

     IN WITNESS WHEREOF, in multiple originals, the undersigned have executed
this Amendment effective as of the Effective Date of this Amendment.

                                         /s/ Brent Ardoin
                                         ---------------------------------------
                                         BRENT ARDOIN

                                                   Amendment Operating Agreement
                                                                   Page 14 of 18
                                                                November 4, 2005

<PAGE>

     IN WITNESS WHEREOF, in multiple originals, the undersigned have executed
this Amendment effective as of the Effective Date of this Amendment.

                                         /s/ Lionel Mayer
                                         ---------------------------------------
                                         LIONEL MAYER

                                                   Amendment Operating Agreement
                                                                   Page 15 of 18
                                                                November 4, 2005

<PAGE>

     IN WITNESS WHEREOF, in multiple originals, the undersigned have executed
this Amendment effective as of the Effective Date of this Amendment.

                                         /s/ Kevin Hargrave
                                         ---------------------------------------
                                         KEVIN HARGRAVE

                                                   Amendment Operating Agreement
                                                                   Page 16 of 18
                                                                November 4, 2005

<PAGE>

     IN WITNESS WHEREOF, in multiple originals, the undersigned have executed
this Amendment effective as of the Effective Date of this Amendment.

                                         /s/ Kerry Thibodeaux
                                         ---------------------------------------
                                         KERRY THIBODEAUX

                                                   Amendment Operating Agreement
                                                                   Page 17 of 18
                                                                November 4, 2005

<PAGE>

     IN WITNESS WHEREOF, in multiple originals, the undersigned have executed
this Amendment effective as of the Effective Date of this Amendment.

                                         /s/ Michael Felton
                                         ---------------------------------------
                                         MICHAEL FELTON

                                                   Amendment Operating Agreement
                                                                   Page 18 of 18
                                                                November 4, 2005