SECURITIES AND EXCHANGE COMMISSION
                              Washington, DC 20549

                                 SCHEDULE 13G/A
                                 (Rule 13d-102)

           INFORMATION TO BE INCLUDED IN STATEMENTS FILED PURSUANT TO
            RULES 13d-1(b), (c) AND (d) AND AMENDMENTS THERETO FILED
                            PURSUANT TO RULE 13d-2(b)

                                (Amendment No. 2)


                                 ARCH COAL, INC.
--------------------------------------------------------------------------------
                                (Name of Issuer)


                Shares of Common Stock, par value $.01 per share
--------------------------------------------------------------------------------
                         (Title of Class of Securities)


                                    039380100
--------------------------------------------------------------------------------
                                 (CUSIP Number)


                                  June 4, 2003
--------------------------------------------------------------------------------
             (Date of Event Which Requires Filing of this Statement)


Check the appropriate box to designate the rule pursuant to which this Schedule
is filed:

        [ ]   Rule 13d-1(b)
        [X]   Rule 13d-1(c)
        [ ]   Rule 13d-1(d)



                                  Page 1 of 7


-------------------------                              -------------------------
CUSIP No. 039380100                  13G/A
-------------------------                              -------------------------

--------------------------------------------------------------------------------
      1        NAME OF REPORTING PERSONS
               I.R.S. IDENTIFICATION NO. OF ABOVE PERSONS (ENTITIES ONLY)

               Greenlight Capital, L.L.C.   13-3886851
--------------------------------------------------------------------------------
      2        CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*       (a) [ ]
                                                                       (b) [ ]
--------------------------------------------------------------------------------
      3        SEC USE ONLY

--------------------------------------------------------------------------------
      4        CITIZENSHIP OR PLACE OF ORGANIZATION

               Delaware
--------------------------------------------------------------------------------
                                5        SOLE VOTING POWER

        NUMBER OF                        0
         SHARES              ---------------------------------------------------
      BENEFICIALLY              6        SHARED VOTING POWER
        OWNED BY
          EACH                           0
       REPORTING             ---------------------------------------------------
      PERSON WITH               7        SOLE DISPOSITIVE POWER

                                         0
                             ---------------------------------------------------
                                8        SHARED DISPOSITIVE POWER

                                         0
--------------------------------------------------------------------------------
      9        AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

               0
--------------------------------------------------------------------------------
     10        CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN
               SHARES*
                                                                        [ ]
--------------------------------------------------------------------------------
     11        PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW 9

               0
--------------------------------------------------------------------------------
     12        TYPE OF REPORTING PERSON*

               OO
--------------------------------------------------------------------------------
         *SEE INSTRUCTIONS BEFORE FILLING OUT
         **SEE ITEM 4(b).



                                  Page 2 of 7


-------------------------                              -------------------------
CUSIP No. 039380100                  13G/A               13-3871632
-------------------------                              -------------------------

--------------------------------------------------------------------------------
      1        NAME OF REPORTING PERSONS
               I.R.S. IDENTIFICATION NO. OF ABOVE PERSONS (ENTITIES ONLY)

               Greenlight Capital, Inc.
--------------------------------------------------------------------------------
      2        CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*        (a) [ ]
                                                                        (b) [ ]
--------------------------------------------------------------------------------
      3        SEC USE ONLY

--------------------------------------------------------------------------------
      4        CITIZENSHIP OR PLACE OF ORGANIZATION

               Delaware
--------------------------------------------------------------------------------
                                5        SOLE VOTING POWER

                                         0
       NUMBER OF             ---------------------------------------------------
         SHARES                 6        SHARED VOTING POWER
      BENEFICIALLY
        OWNED BY                         0
          EACH               ---------------------------------------------------
       REPORTING                7        SOLE DISPOSITIVE POWER
      PERSON WITH
                                         0
                             ---------------------------------------------------
                                8        SHARED DISPOSITIVE POWER

                                         0
--------------------------------------------------------------------------------
      9        AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

               0
--------------------------------------------------------------------------------
     10        CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN
               SHARES*
                                                                        [ ]
--------------------------------------------------------------------------------
     11
               PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW 9

               0
--------------------------------------------------------------------------------
     12        TYPE OF REPORTING PERSON*

               CO
--------------------------------------------------------------------------------
         *SEE INSTRUCTIONS BEFORE FILLING OUT
         **SEE ITEM 4(b).



                                  Page 3 of 7


-------------------------                              -------------------------
CUSIP No. 039380100                  13G/A
-------------------------                              -------------------------

--------------------------------------------------------------------------------
      1        NAME OF REPORTING PERSONS
               I.R.S. IDENTIFICATION NO. OF ABOVE PERSONS (ENTITIES ONLY)

               David Einhorn
--------------------------------------------------------------------------------
      2        CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*       (a) [ ]
                                                                       (b) [ ]
--------------------------------------------------------------------------------
      3        SEC USE ONLY

--------------------------------------------------------------------------------
      4        CITIZENSHIP OR PLACE OF ORGANIZATION

               U.S. Citizen
--------------------------------------------------------------------------------
                                5        SOLE VOTING POWER

                                         0
        NUMBER OF            ---------------------------------------------------
         SHARES                 6        SHARED VOTING POWER
      BENEFICIALLY
        OWNED BY                         0
          EACH               ---------------------------------------------------
       REPORTING                7        SOLE DISPOSITIVE POWER
      PERSON WITH
                                         0
                             ---------------------------------------------------
                                8        SHARED DISPOSITIVE POWER

                                         0
--------------------------------------------------------------------------------
      9        AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

               0
--------------------------------------------------------------------------------
     10        CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN
               SHARES*
                                                                        [ ]
--------------------------------------------------------------------------------
     11
               PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW 9

               0
--------------------------------------------------------------------------------
     12        TYPE OF REPORTING PERSON*

               IN
--------------------------------------------------------------------------------
         *SEE INSTRUCTIONS BEFORE FILLING OUT
         **SEE ITEM 4(b).



                                  Page 4 of 7



                         AMENDMENT NO. 2 TO SCHEDULE 13G

         This Amendment No. 2 to Schedule 13G (the "Amendment"), relating to
shares of common stock of Arch Coal, Inc., a Delaware corporation (the
"Issuer"), is being filed with the Securities and Exchange Commission as an
amendment to the Schedule 13G filed on August 16, 2002, as amended by Amendment
Number 1 thereto, filed March 18, 2003 (the "Schedule 13G"). This Amendment is
being filed on behalf of Greenlight Capital, L.L.C., a Delaware limited
liability company ("Greenlight LLC"), Greenlight Capital, Inc., a Delaware
corporation ("Greenlight Inc." and together with Greenlight LLC, "Greenlight")
and Mr. David Einhorn, principal of Greenlight.

         This Schedule 13G relates to shares of Common Stock of the Issuer
purchased by Greenlight for the account of (i) Greenlight Capital, L.P., of
which Greenlight LLC is the general partner, (ii) Greenlight Capital Qualified,
L.P., of which Greenlight LLC is the general partner and (iii) Greenlight
Capital Offshore, Ltd., to which Greenlight Inc. acts as investment advisor.

ITEM 4   OWNERSHIP.

Item 4 of the Schedule 13G is hereby amended and restated in its entirety as
follows:

         (a)      Greenlight and Mr. Einhorn are the beneficial owners of 0
                  shares of Common Stock.

         (b)      Greenlight and Mr. Einhorn are the beneficial owners of 0% of
                  the outstanding shares of Common Stock.

         (c)      Greenlight has the sole power to vote and dispose of the 0
                  shares of Common Stock beneficially owned by it. As the
                  principal of Greenlight, Mr. Einhorn may direct the vote and
                  disposition of the 0 shares of Common Stock beneficially owned
                  by Greenlight.

ITEM 5   OWNERSHIP OF FIVE PERCENT OR LESS OF A CLASS.

Item 5 of the Schedule 13G is amended and restated in its entirety to read as
follows:

         If this Statement is being filed to report the fact that as of the date
         hereof the reporting person has ceased to be the beneficial owner of
         more than five percent of the class of securities, check the following.
         [X]

ITEM 10 CERTIFICATION.

         By signing below I certify that, to the best of my knowledge and
         belief, the securities referred to above were not acquired and are not
         held for the purpose of or with the effect of changing or influencing
         the control of the issuer of the securities and were not acquired and
         are not held in connection with or as a participant in any transaction
         having that purpose or effect.



                                  Page 5 of 7



EXHIBITS        EXHIBIT 1
                ---------

                Joint Filing Agreement dated October 2, 2003, among Greenlight
                LLC, Greenlight Inc. and David Einhorn.



                                  Page 6 of 7


                                    SIGNATURE

         After reasonable inquiry and to the best of my knowledge and belief, I
certify that the information set forth in this statement is true, complete and
correct.


         Date:  October 2, 2003


                                              Greenlight Capital, L.L.C.


                                              By: /S/ DAVID EINHORN
                                                  ------------------------------
                                                  David Einhorn, Managing Member


                                              Greenlight Capital, Inc.


                                              By: /S/ DAVID EINHORN
                                                  ------------------------------
                                                  David Einhorn, President


                                              /S/ DAVID EINHORN
                                              ----------------------------------
                                              David Einhorn



                                  Page 7 of 7



                               INDEX TO EXHIBITS




EXHIBIT
NUMBER                            DESCRIPTION
---------               -------------------------------------------------------
                     
Exhibit 1               Joint Filing Agreement dated October 2, 2003, among
                        Greenlight LLC, Greenlight Inc. and David Einhorn.