EXHIBIT 99

                             LETTER OF TRANSMITTAL

                        To Tender Shares of Common Stock
                                       of
                            CONCHO BANCSHARES, INC.
              Pursuant to the Offer for all Outstanding Shares of
                                Common Stock of
                           Concho Bancshares, Inc. by
                        FIRST FINANCIAL BANKSHARES, INC.

       ================================================================
                 THE EXCHANGE OFFER WILL EXPIRE AT 5:00 P.M.,
                       TEXAS TIME, ON MARCH 10, 1994,
                   UNLESS EXTENDED (THE "EXPIRATION DATE").
       ================================================================

                         ------------------------------

     PURSUANT TO THE OFFERING CIRCULAR/PROSPECTUS DATED FEBRUARY 8, 1994

  TO:  TRUST DEPARTMENT OF FIRST NATIONAL BANK OF ABILENE, The Exchange Agent

                      By Hand, Mail or Overnight Courier:

                                Trust Department
                         First National Bank of Abilene
                                  Third Floor
                                400 Pine Street
                              Abilene, Texas 79601

                     For information call:  (915) 675-7100
                                            --------------

     DELIVERY OF THIS INSTRUMENT TO AN ADDRESS OTHER THAN AS SET FORTH ABOVE OR
TRANSMISSION OF INSTRUCTIONS VIA A FACSIMILE NUMBER OTHER THAN THE ONE LISTED
ABOVE WILL NOT CONSTITUTE A VALID DELIVERY.  THE INSTRUCTIONS ACCOMPANYING THIS
LETTER OF TRANSMITTAL SHOULD BE READ CAREFULLY BEFORE THIS LETTER OF TRANSMITTAL
IS COMPLETED.

     The undersigned acknowledges that he or she has received the Offering
Circular/Prospectus dated February 8, 1994 (the "Prospectus") of First
Financial Bankshares, Inc. ("First Financial") and this letter of transmittal
(the "Letter of Transmittal"), which constitutes First Financial's offer (the
"Exchange Offer") to exchange shares of its voting common stock, par value
$10.00 per share ("First Financial Common Stock"), which have been registered
under the Securities Act of 1933, as amended (the "Securities Act"), pursuant to
a Registration Statement of which the Prospectus is a part, for all of the
issued and outstanding shares of Concho Bancshares, Inc. ("Concho"), par value
$0.50 per share ("Concho Common Stock").  Other capitalized terms used but not
defined herein have the meaning given to them in the Prospectus.

     This Letter of Transmittal is to be used by Concho Shareholders (as defined
below) if certificates representing Concho Common Stock are to be physically
delivered herewith or if the guaranteed delivery procedures described in the

                                      -1-

 
Prospectus are to be utilized pursuant to the procedures set forth in "The
Exchange Offer -- Exchange of Shares and Certificates" and "--Guaranteed
Delivery Procedures" in the Prospectus.

     The term "Concho Shareholder" with respect to the Exchange Offer means any
person in whose name shares of Concho Common Stock are registered on the books
of Concho or any other person who has obtained a properly completed stock power
from the registered Concho Shareholder.  The undersigned has completed, executed
and delivered this Letter of Transmittal to indicate the action that the
undersigned desires to take with respect to the Exchange Offer. Concho
Shareholders who wish to tender their Concho Common Stock must complete this
Letter of Transmittal in its entirety.

                   NOTE:  SIGNATURES MUST BE PROVIDED BELOW.
                 PLEASE READ THIS ENTIRE LETTER OF TRANSMITTAL
                    CAREFULLY BEFORE CHECKING ANY BOX BELOW.

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              DESCRIPTION OF SHARES OF CONCHO COMMON STOCK TENDERED
- --------------------------------------------------------------------------------
 
 
                                                                   Total Number
                                                                   of Shares of
                                                                      Concho
                                                                   Common Stock
Name(s) and Address(es) of Registered Holder(s)    Certificate    Represented by
         (Please fill in, if blank)                 Number(s)      Certificates
                                                             
- --------------------------------------------------------------------------------
 
- --------------------------------------------------------------------------------
 
- --------------------------------------------------------------------------------
 
- --------------------------------------------------------------------------------
 
- --------------------------------------------------------------------------------
 
- --------------------------------------------------------------------------------
 
  If the space provided above is inadequate, list the certificate numbers and
   principal amounts on a separate signed schedule and affix the list to this
   Letter of Transmittal.
================================================================================
 
 
[ ]  CHECK HERE IF TENDERED SHARES ARE BEING DELIVERED PURSUANT TO A NOTICE OF
     GUARANTEED DELIVERY PREVIOUSLY SENT TO THE EXCHANGE AGENT AND COMPLETE THE
     FOLLOWING:

     Name(s) of Tendering Shareholder(s): 
                                          --------------------------------------

     Date of Execution of Notice of Guaranteed Delivery: 
                                                         -----------------------

     Name of Institution which Guaranteed Delivery: 
                                                    ----------------------------


Ladies and Gentlemen:

        Subject to the terms and conditions of the Exchange Offer set forth in
the Prospectus (receipt of which is hereby acknowledged), the undersigned hereby
tenders to First Financial the shares of Concho Common Stock described herein. 
Subject to and effective upon the acceptance for exchange of the shares of
Concho Common Stock tendered in accordance with this Letter of Transmittal, the
undersigned sells, assigns and transfers to, or upon the order of, First
Financial all right, title and interest in and to all the shares of Concho
Common Stock tendered hereby.  The undersigned hereby irrevocably constitutes
and appoints the Exchange Agent its true and lawful agent and attorney-in-fact

                                      -2-

 
with respect to the tendered shares of Concho Common Stock with full power of
substitution to (i) deliver certificates for such shares of Concho Common Stock
with all accompanying evidences of transfer and authenticity to, or upon the
order of, First Financial and (ii) present such shares of Concho Common Stock
for transfer on the books of Concho and receive all benefits and otherwise
exercise all rights of beneficial ownership of such shares of Concho Common
Stock all in accordance with the terms of the Exchange Offer.  The power of
attorney granted in this paragraph shall be deemed irrevocable and coupled with
an interest.

        For purposes of the Exchange Offer, First Financial shall be deemed to
have accepted validly tendered shares of Concho Common Stock when, as and if
First Financial has given oral or written notice thereof to the Exchange Agent.

        If any tendered shares of Concho Common Stock are not accepted for
exchange pursuant to the Exchange Offer for any reason, certificates for any
such unaccepted shares of Concho Common Stock will be returned, without expense,
to the undersigned at the address shown below or at a different address as may
be indicated herein under "Special Delivery Instructions" as promptly as
practicable after the Expiration Date.

        The undersigned hereby represents and warrants that the undersigned has
full power and authority to tender, sell, assign and transfer the shares of
Concho Common Stock tendered hereby and that when the same are accepted for
exchange by First Financial, First Financial shall acquire good and unencumbered
title thereto, free and clear of all liens, restrictions, charges and
encumbrances and not subject to any adverse claim.  The undersigned will, upon
request, execute and deliver any additional documents deemed by the Exchange
Agent or First Financial to be necessary or desirable to complete the sale,
assignment and transfer of the shares of Concho Common Stock tendered hereby.

        The undersigned hereby irrevocably appoints Curtis R. Harvey the
attorney and proxy of the undersigned, with full power of substitution, to
exercise all voting and other rights of the undersigned in such manner as such
attorney and proxy or his substitute shall in his sole discretion deem proper,
with respect to all of the shares of Concho Common Stock tendered hereby which
have been acquired by First Financial pursuant to the Exchange Offer prior to
the time of any vote or other action, at any meeting of Concho Shareholders
(whether annual or special and whether or not an adjourned meeting), by written
consent or otherwise.  This proxy is irrevocable and is granted in consideration
of, and is effective upon, the acquisition of such shares of Concho Common Stock
by First Financial in accordance with the terms of the Exchange Offer.  Such
acquisition shall revoke any other proxy or written consent granted by the
undersigned at any time with respect to such shares of Concho Common Stock, and
no subsequent proxies will be given or written consents will be executed by the
undersigned (and if given or executed, will not be deemed to be effective).

        All authority conferred or agreed to be conferred by this Letter of
Transmittal shall survive the death, incapacity or dissolution of the
undersigned, and every obligation of the undersigned under this Letter of
Transmittal shall be binding upon the undersigned's heirs, personal
representatives, successors and assigns.  Except as stated in the Exchange
Offer, this tender is irrevocable.

        The undersigned understands that tenders of shares of Concho Common
Stock pursuant to the procedures described under the caption "The Exchange
Offer" in the Prospectus and in the instructions hereto will constitute a
binding agreement between the undersigned and First Financial upon the terms and
subject to the conditions of the Exchange Offer.

        Unless otherwise indicated under "Special Exchange Instructions," please
issue the certificates representing the shares of First Financial Common Stock
issued in exchange for the shares of Concho Common Stock accepted for exchange
and any cash payment in lieu of fractional shares, as discussed

                                      -3-

 
in the Prospectus, and return any shares of Concho Common Stock not exchanged,
in the name(s) of the undersigned.  Similarly, unless otherwise indicated under
"Special Delivery Instructions," please send the certificates representing the
shares of First Financial Common Stock issued in exchange for the shares of
Concho Common Stock accepted for exchange and any certificates for shares of
Concho Common Stock not exchanged (and accompanying documents, as appropriate)
to the undersigned at the address shown below the undersigned's signatures.  In
the event that both "Special Exchange Instructions" and "Special Delivery
Instructions" are completed, please issue the certificates representing the
shares of First Financial Common Stock issued in exchange for the shares of
Concho Common Stock accepted for exchange and return any shares of Concho Common
Stock not exchanged in the name(s) of, and send said certificates to, the
person(s) so indicated.  The undersigned recognizes that First Financial has no
obligation pursuant to the "Special Exchange Instructions" and "Special Delivery
Instructions" to transfer any shares of Concho Common Stock from the name of the
registered holder(s) thereof if First Financial does not accept for exchange any
of the shares of Concho Common Stock so tendered.

================================================================================
                         SPECIAL EXCHANGE INSTRUCTIONS
                         (See Instructions 3, 4 and 5)

To be completed ONLY if certificates for shares of First Financial Common Stock
or the check for any cash payment in lieu of fractional shares of First
Financial Common Stock are to be issued in the name of someone other than the
undersigned.
                                                             
Issue certificate(s) to:                                     
                                                             
Name                                                         
    ----------------------------------------------------------------------------
                                (Please Print)
                                                             
Address                                                      
       -------------------------------------------------------------------------
                                                             
- --------------------------------------------------------------------------------
                              (Include Zip Code)
                                                             
                                                             
- --------------------------------------------------------------------------------
                  (Tax Identification or Social Security No.)
                                                             
================================================================================

================================================================================
                         SPECIAL DELIVERY INSTRUCTIONS
                         (See Instructions 3, 4 and 5)
                   
To be completed ONLY if certificates for shares of First Financial Common Stock,
the check for any cash payment in lieu of fractional shares of First Financial
Common Stock, or certificates for shares of Concho Common Stock not accepted are
to be sent to someone other than the undersigned, or to the undersigned at an
address other than that shown above.

Mail to:

Name
    ----------------------------------------------------------------------------
                                (Please Print)
                 
Address          
       -------------------------------------------------------------------------
                 
- --------------------------------------------------------------------------------
                              (Include Zip Code)

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       Concho Shareholders who wish to tender their shares of Concho Common    
Stock and (i) whose shares of Concho Common Stock are not immediately available,
or (ii) who cannot deliver their shares of Concho Common Stock, this Letter of 
Transmittal or any other documents required hereby to the Exchange Agent prior 
to the Expiration Date, may tender their shares of Concho Common Stock according
to the guaranteed delivery procedures set forth in the Prospectus under the
caption "The Exchange Offer -- Guaranteed Delivery Procedures."  See Instruction
1 regarding the completion of this Letter of Transmittal.

                                      -4-

 
                               PLEASE SIGN HERE
                  (PLEASE COMPLETE SUBSTITUTE FORM W-9 BELOW)

X
- -------------------------------------------    ----------------------
                                                              Date
                                           
X                                          
- -------------------------------------------    ----------------------
       Signature(s) of Registered Holder(s)                   Date
          or Authorized Signatory

Area Code and Telephone Number:                                 
                               -------------------------------

        The above lines must be signed by the registered holder(s) of shares of
Concho Common Stock as their name(s) appear(s) on the certificates reflecting
shares of Concho Common Stock or by person(s) authorized to become registered
holder(s).  If signature is by a trustee, executor, administrator, guardian,
attorney-in-fact, officer of a corporation or other person acting in a fiduciary
or representative capacity, such person must set forth his or her full title
below.  See Instruction 3 regarding the completion of this Letter of
Transmittal.

Name(s):
          --------------------------------------------------------------
                                                                        
          --------------------------------------------------------------
                                (Please Print)
                                                                        
Capacity:                                                               
          --------------------------------------------------------------
                                                                        
Address:                                                                
          --------------------------------------------------------------
                              (Include Zip Code)                        
                                                                        
          SIGNATURE(S) GUARANTEED BY AN ELIGIBLE INSTITUTION (AS DEFINED
          BELOW):                                                       
          (IF REQUIRED BY INSTRUCTION 3)                                
                                                                        
                                                                        
          --------------------------------------------------------------
                            (Authorized Signature)
                                                                        
          --------------------------------------------------------------
                                    (Title)
                                                                        
          --------------------------------------------------------------
                                (Name of Firm)
                                                                        
          --------------------------------------------------------------
                        (Address, Including Zip Code)                   
                                                                        
          --------------------------------------------------------------
                      (Area Code and Telephone Number)

          Dated:                       , 1994
                -----------------------

                                      -5-

 
        Under the federal income tax laws, the Exchange Agent may be required to
withhold 31% of the amount of any payments made to certain Concho Shareholders
pursuant to the Exchange Offer.  In order to avoid such backup withholding, each
tendering Concho Shareholder must provide the Exchange Agent with such Concho
Shareholder's correct taxpayer identification number by completing the
Substitute Form W-9 set forth below.  In general, if a Concho Shareholder is an
individual, the taxpayer identification number is the Social Security number of
such individual.  If the Exchange Agent is not provided with the correct
taxpayer identification number, the Concho Shareholder may be subject to a $50
penalty imposed by the Internal Revenue Service.  CERTAIN CONCHO SHAREHOLDERS
(INCLUDING, AMONG OTHERS, ALL CORPORATIONS AND CERTAIN FOREIGN INDIVIDUALS) ARE
NOT SUBJECT TO THESE BACKUP WITHHOLDING AND REPORTING REQUIREMENTS.  In order to
satisfy the Exchange Agent that a foreign individual qualifies as an exempt
recipient, such Concho Shareholder must submit a statement, signed under
penalties of perjury, attesting to that individual's exempt status.  A form for
such statements can be obtained from the Exchange Agent.  For further
information concerning backup withholding and instructions for completing the
Substitute Form W-9 (including how to obtain a taxpayer identification number if
you do not have one and how to complete the Substitute Form W-9 if securities
are held in more than one name), consult the enclosed Guideline of the Internal
Revenue Service for Certification of Taxpayer Identification Number on
Substitute Form W-9.

        Failure to complete the Substitute Form W-9 will not, by itself, cause
shares of Concho Common Stock to be deemed invalidly tendered, but may require
the Exchange Agent to withhold 31% of the amount of any payments made pursuant
to the Exchange Offer.  Backup withholding is not an additional federal income
tax.  Rather, the federal income tax liability of a person subject to backup
withholding will be reduced by the amount of tax withheld.  If withholding
results in an overpayment of taxes, a refund may be obtained.

        PAYER'S NAME: TRUST DEPARTMENT OF FIRST NATIONAL BANK OF ABILENE
================================================================================
       SUBSTITUTE                 
        Form W-9                  
Department of the Treasury                          REQUEST FOR TAXPAYER
 Internal Revenue Service                IDENTIFICATION NUMBER AND CERTIFICATION
Payer's Request for Taxpayer
 Identification No.
- --------------------------------------------------------------------------------
PART I  Taxpayer Identification Number (TIN)          PART II  For Payees Exempt
                                                                from Backup
                                                                Withholding (see
                                                                enclosed 
                                                                Guidelines)
- --------------------------------------------------------------------------------
Enter your TIN on the         Social security number:       
 appropriate line.  For                                     
 individuals, this is         -------------------------------
 your social security                   OR                  
 number (SSN).  For other     Employer identification number:
 entities, it is your                                       
 employer identification      -------------------------------
 number (EIN).
- --------------------------------------------------------------------------------
 
CERTIFICATION.--Under penalties of perjury, I certify that:
 
1.  The number shown on this form is my correct taxpayer identification number
(or I am waiting for a number to be issued to me), AND
 
2.  I am not subject to backup withholding because: (a) I am exempt from backup
withholding, or (b) I have not been notified by the Internal Revenue Service
that I am subject to backup withholding as a result of a failure to report all
interest or dividends, or (c) the IRS has notified me that I am no longer
subject to backup withholding.
 
CERTIFICATION INSTRUCTIONS.--You must cross out item 2 above if you have been
notified by the IRS that you are currently subject to backup withholding because
of underreporting interest or dividends on your tax return.  However, if after
being notified by the IRS that you were subject to backup withholding you
received another notification from the IRS that you are no longer subject to
backup withholding, do not cross out item 2.
 
Name (if joint names, list first and circle  the name of the person or entity
whose number you enter in Part I below.
                                        ----------------------------------------

Address (number and street)
                            ----------------------------------------------------
                      
City, state, and ZIP code
                          ------------------------------------------------------

Signature                                           Date
          ---------------------------------------        -----------------------

================================================================================

                                      -6-

 
IF YOU CHECKED THE BOX IN PART II OF THE SUBSTITUTE FORM W-9, YOU MUST SIGN AND
DATE THE FOLLOWING CERTIFICATION:

        CERTIFICATION OF PAYEE AWAITING TAXPAYER IDENTIFICATION NUMBER

================================================================================
  I certify, under penalties of perjury, that a Taxpayer Identification Number
  has not been issued to me, and that I mailed or delivered an application to
  receive a Taxpayer Identification Number to the appropriate IRS Center or
  Social Security Administration Office (or I intend to mail or deliver an
  application in the near future). I understand that if I do not provide a
  Taxpayer Identification Number within sixty (60) days, 31% of all reportable
  payments made to me thereafter will be withheld until I provide a number.
 
     SIGNATURE                                           DATE
               --------------------------------------         ----------------

================================================================================

NOTE: FAILURE TO COMPLETE AND RETURN THIS FORM MAY RESULT IN BACKUP
      WITHHOLDING OF 31% OF ANY PAYMENTS MADE TO YOU PURSUANT TO THIS EXCHANGE
      OFFER. PLEASE REVIEW THE ENCLOSED GUIDELINES FOR CERTIFICATION OF TAXPAYER
      IDENTIFICATION NUMBER ON SUBSTITUTE FORM W-9 FOR ADDITIONAL DETAILS.

                                      -7-

 
                                 INSTRUCTIONS

        FORMING PART OF THE TERMS AND CONDITIONS OF THE EXCHANGE OFFER


      1.   DELIVERY OF THIS LETTER OF TRANSMITTAL AND SHARES OF CONCHO COMMON
STOCK.  The certificates for the tendered shares of Concho Common Stock, as well
as a properly completed and duly executed copy of this Letter of Transmittal and
any other documents required by this Letter of Transmittal must be received by
the Exchange Agent at its address set forth herein prior to 5:00 P.M., Texas
time, on the Expiration Date.  Subject to certain conditions to the consummation
of the Exchange Offer, the exchange of shares of First Financial Common Stock
for shares of Concho Common Stock will be promptly made with respect to all
shares of Concho Common Stock properly tendered on or prior to 5:00 p.m., Texas
time, on the Expiration Date, if First Financial receives notice from the
Exchange Agent that at least 90% of the outstanding shares of Concho Common
Stock have been tendered.  The method of delivery of the tendered shares of
Concho Common Stock, this Letter of Transmittal and all other required documents
to the Exchange Agent is at the election and risk of the Concho Shareholder and,
except as otherwise provided below, the delivery will be deemed made only when
actually received by the Exchange Agent.  Instead of delivery by mail, it is
recommended that the Concho Shareholder use an overnight or hand delivery
service.  If certificates for shares of Concho Common Stock are sent by mail,
registered mail with return receipt requested, properly insured, is recommended.
In all cases, sufficient time should be allowed to assure timely delivery.

      Concho Shareholders who wish to tender their shares of Concho Common Stock
and (i) whose shares of Concho Common Stock are not immediately available, or
(ii) who cannot deliver their shares of Concho Common Stock, this Letter of
Transmittal or any other documents required hereby to the Exchange Agent prior
to the Expiration Date must tender their shares of Concho Common Stock pursuant
to the guaranteed delivery procedures set forth in the Prospectus.  Pursuant to
such procedures:

      (i) such tender must be made by or through a firm which is a member of a
      registered national securities exchange or the National Association of
      Securities Dealers, Inc., or by a commercial bank or trust company having
      an office or correspondent in the United States (an "Eligible
      Institution");

      (ii) prior to the Expiration Date, the Exchange Agent must have received
      from the Eligible Institution a properly completed and duly executed
      Notice of Guaranteed Delivery (by facsimile transmission, mail or hand
      delivery) setting forth the name and address of the holder of the shares
      of Concho Common Stock, the certificate number for the certificates
      representing such shares of Concho Common Stock and the amount of shares
      of Concho Common Stock tendered, stating that the tender is being made
      thereby and guaranteeing that, within 5 business days after the Expiration
      Date, this Letter of Transmittal together with the certificate(s)
      representing the shares of Concho Common Stock and any other required
      documents will be deposited by the Eligible Institution with the Exchange
      Agent; and

      (iii) such properly completed and executed Letter of Transmittal, as well
      as all other documents required by this Letter of Transmittal and the
      certificate(s) representing all tendered shares of Concho Common Stock in
      proper form for transfer, must be received by the Exchange Agent within 5
      business days after the Expiration Date, all as provided in the Prospectus
      under the caption "The Exchange Offer -- Guaranteed Delivery Procedures."

Any Concho Shareholder who wishes to tender his or her shares of Concho Common
Stock pursuant to the guaranteed delivery procedures described above must ensure
that the Exchange Agent receives the Notice of Guaranteed Delivery prior to 5:00
P.M., Texas time, on the Expiration Date.

      All questions as to the validity, form, eligibility (including time of
receipt), acceptance and withdrawal of tendered shares of Concho Common Stock
will be determined by First Financial in its sole discretion, which
determination will be final and binding.  First Financial reserves the absolute
right to reject any and all shares of Concho Common Stock not properly tendered
or any shares of Concho

                                      -8-

 
Common Stock First Financial's acceptance of which would, in the opinion of
counsel for First Financial, be unlawful.  First Financial also reserves the
right to waive any irregularities or conditions of tender as to particular
shares of Concho Common Stock.  Unless waived, any defects or irregularities in
connection with tenders of shares of Concho Common Stock must be cured within
such time as First Financial shall determine.  Neither First Financial, the
Exchange Agent nor any other person shall be under any duty to give notification
of defects or irregularities with respect to tenders of shares of Concho Common
Stock, nor shall any of them incur any liability for failure to give such
notification.  Tenders of shares of Concho Common Stock will not be deemed to
have been made until such defects or irregularities have been cured or waived. 
Any shares of Concho Common Stock received by the Exchange Agent that are not
properly tendered and as to which the defects or irregularities have not been
cured or waived will be returned without cost by the Exchange Agent to the
tendering Concho Shareholders, unless otherwise provided in this Letter of
Transmittal, as soon as practicable following the Expiration Date.

      2.   NO PARTIAL TENDERS.  All shares of Concho Common Stock represented by
certificates delivered to the Exchange Agent will be deemed to have been
tendered.

      3.   SIGNATURES ON THE LETTER OF TRANSMITTAL; STOCK POWERS AND
ENDORSEMENTS; GUARANTEE OF SIGNATURES.  If this Letter of Transmittal is signed
by the registered holder(s) of the shares of Concho Common Stock tendered
hereby, the signature must correspond with the name(s) as written on the face of
the certificates representing the shares of Concho Common Stock without
alteration, enlargement or any change whatsoever.

      If this Letter of Transmittal is signed by the registered holder(s) of
shares of Concho Common Stock tendered and the certificate(s) for shares of
First Financial Common Stock issued in exchange therefor is to be issued to the
registered holder, such holder need not and should not endorse any certificates
for tendered shares of Concho Common Stock, nor provide a separate stock power. 
In any other case, such holder must either properly endorse the certificates
representing shares of Concho Common Stock tendered or transmit a properly
completed separate stock power with this Letter of Transmittal, with the
signatures on the endorsement or stock power guaranteed by an Eligible
Institution.

      If any shares of Concho Common Stock tendered hereby are held of record by
two or more persons, all such persons must sign this Letter of Transmittal.

      If this Letter of Transmittal is signed by a person other than the
registered holder(s) of any certificates for shares of Concho Common Stock
tendered hereby, such certificates for shares of Concho Common Stock must be
endorsed or accompanied by appropriate stock powers signed exactly as the name
of the registered holder(s) appears on the certificates representing such shares
of Concho Common Stock.

      If this Letter of Transmittal or any certificates for shares of Concho
Common Stock or stock powers are signed by trustees, executors, administrators,
guardians, attorneys-in-fact, or officers of corporations or others acting in a
fiduciary or representative capacity, such persons should so indicate when
signing, and unless waived by First Financial, evidence satisfactory to First
Financial of their authority so to act must be submitted with this Letter of
Transmittal.

      Endorsements on certificates for shares of Concho Common Stock and
signatures on stock powers required by this Instruction 3 must be guaranteed by
an Eligible Institution.

      Signatures on this Letter of Transmittal must be guaranteed by an Eligible
Institution unless the shares of Concho Common Stock tendered pursuant thereto
are tendered (i) by a registered holder who has not completed the box set forth
herein entitled "Special Exchange Instructions" or the box entitled "Special
Delivery Instructions" or (ii) for the account of an Eligible Institution.

      4.   SPECIAL EXCHANGE AND DELIVERY INSTRUCTIONS.  If the certificates for
shares of First Financial Common Stock or checks for any cash payment in lieu of
payment of fractional shares of First Financial Common Stock are to be issued,
or any shares of Concho Common Stock not accepted for

                                      -9-

 
exchange are to be mailed to someone other than the person(s) signing this
Letter of Transmittal or to the person(s) signing this Letter of Transmittal at
an address other than that provided herein, the appropriate boxes on this Letter
of Transmittal should be completed.  In the case of issuance in a different
name, the taxpayer identification or social security number of the person named
must also be indicated.

      5.   TRANSFER TAXES.  First Financial will pay all transfer taxes, if any,
applicable to the exchange of shares of Concho Common Stock pursuant to the
Exchange Offer unless such payment would jeopardize the tax-free nature of the
Exchange Offer or the Merger (as defined in the Prospectus) for Federal income
tax purposes.  If, however, certificates representing shares of First Financial
Common Stock or checks for any cash payment in lieu of fractional shares of
First Financial Common Stock are issued, or certificates for shares of Concho
Common Stock not accepted for exchange are to be returned, in the name of any
person other than the registered holder of the shares of Concho Common Stock
tendered hereby, or if tendered shares of Concho Common Stock are registered in
the name of any person other than the person signing this Letter of Transmittal,
or if a transfer tax is imposed for any reason other than the exchange of shares
of Concho Common Stock pursuant to the Exchange Offer, then the amount of any
such transfer taxes (whether imposed on the registered holder or any other
persons) will be payable by the tendering holder.  If satisfactory evidence of
payment of such taxes or exemption therefrom is not submitted with this Letter
of Transmittal, the amount of such transfer taxes will be deducted from the
consideration to be received by such holder (i.e., the number of shares of First
Financial Common Stock to be issued to such holder will be reduced).

      6.   WAIVER OF CONDITIONS.  First Financial reserves the absolute right to
amend, waive or modify specified conditions in the Exchange Offer in the case of
any shares of Concho Common Stock tendered.

      7.   MUTILATED, LOST, STOLEN OR DESTROYED SHARES OF CONCHO COMMON STOCK. 
Any tendering holder whose shares of Concho Common Stock have been mutilated,
lost, stolen or destroyed should contact the Exchange Agent at the address
indicated herein for further instruction.

      8.   REQUESTS FOR ASSISTANCE OR ADDITIONAL COPIES.  Questions and requests
for assistance and requests for additional copies of the Prospectus or this
Letter of Transmittal may be directed to the Exchange Agent at the address
specified in the Prospectus.  Concho Shareholders may also contact their broker,
dealer, commercial bank, trust company or other nominee for assistance
concerning the Exchange Offer.

                                     -10-

 
                         (DO NOT WRITE IN SPACE BELOW)

Date Received                Accepted By                 Checked By
              -----------                -----------                -----------
 
================================================================================
 
 

Shares Surrendered     Shares Accepted     Shares Returned     Certificate No.
- ------------------     ---------------     ---------------     ---------------
                                                        

- --------------------------------------------------------------------------------
 
- --------------------------------------------------------------------------------
 
- --------------------------------------------------------------------------------
 
- --------------------------------------------------------------------------------

- --------------------------------------------------------------------------------

 

Delivery Prepared by                           Checked by
                     -----------------------              -----------------
Date
     --------------------
================================================================================

                                     -11-