Washington, D.C. 20549

                                    FORM 8-K

                                 CURRENT REPORT

                Pursuant to Section 13 or 15(d) of the Securities
                              Exchange Act of 1934

         Date of Report (Date of earliest event reported): July 22, 1998

                                 ARCH COAL, INC.
             (Exact name or registrant as specified in its charter)

   Delaware                     1-13105             43-0921172
(State or other             (Commission file      (I.R.S. Employer
jurisdiction of                number)                 ID No.)

               CityPlace One, Suite 300, St. Louis, Missouri 63141
               (Address of principal executive offices) (zip code)

       Registrant's telephone number, including area code: (314) 994-2700

                                Page 1 of 4 pages

                             Exhibit Index on page 4

Item 5.     Other Events.

            On July 22, 1998,  Arch Coal,  Inc.  ("Arch  Coal")  announced  that
Ashland,  Inc., the owner of approximately 55% of Arch Coal's outstanding common
stock,  pursuant  to  registration  rights  held by it under  an  April 4,  1997
Registration  Rights Agreement,  will register  approximately 2.1 million common
shares with the Securities and Exchange  Commission for sale in an  underwritten
public offering.

            A copy of Arch Coal's July 22, 1998 press release is filed  herewith
as an exhibit and incorporated herein by reference.

Item 7.     Financial Statements, Pro Forma Financial Information and Exhibits.

            (c) Exhibits. The following exhibit is filed as part of this Current
Report on Form 8-K:

      Description                         Exhibit No.
      -----------                         -----------

      Press Release dated                 99.1
      July 22, 1998

                                Page 2 of 4 pages


      Pursuant  to the  requirements  of Section  13 or 15(d) of the  Securities
Exchange Act of 1934, the registrant has duly caused this report to be signed on
its behalf by the undersigned, thereunto duly authorized.

                                           ARCH COAL, INC.

                                     BY:   /s/ Jeffry N. Quinn
                                           Jeffry N. Quinn
                                           Senior Vice President -
                                           Law & Human Resources,
                                           Secretary and General Counsel

                                     DATE:  July 22, 1998

                                Page 3 of 4 pages

                                  EXHIBIT INDEX

Exhibit Number          Description                   
- --------------          -------------------------    
99.1                    Press Release dated          
                        July 22, 1998

                                Page 4 of 4 pages

                                                                    Exhibit 99.1


      St. Louis,  MO - Arch Coal, Inc.  (NYSE:ACI)  today announced that Ashland
Inc.,  pursuant  to  registration  rights  held by it under  an  April  4,  1997
registration  rights  agreement,  will register with the Securities and Exchange
Commission (SEC) up to 2,100,000 shares of Arch Coal, Inc. common stock for sale
in an  underwritten  public  offering.  The  sale of  such  shares  will  reduce
Ashland's  ownership  percentage in Arch Coal,  Inc. from  approximately  55% to
approximately  49%. It is anticipated that a registration  statement relating to
these securities will be filed with the SEC in August 1998.

      Any offering will be made only by means of a written prospectus,  and this
release shall not constitute an offer to sell or the solicitation of an offer to
buy, nor shall there be any sale of these  securities in any state in which such
offer,  solicitation  or  sale  would  be  unlawful  prior  to  registration  or
qualification under the securities laws of any such state.

      Arch Coal is the nation's  second  largest coal producer  with  subsidiary
operations in West Virginia, Kentucky, Virginia, Illinois, Wyoming, Colorado and
Utah. Through these operations, Arch Coal provides the fuel for approximately 6%
of U.S. electric power generation.