------------------------------
                                                           OMB APPROVAL
                                                  ------------------------------
                                                  OMB Number           
                                                  Expires:        
                                                  Estimated average burden
                                                  hours per response ....... 0.5
                                                  ------------------------------

                     U.S. SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                     FORM 4

                  STATEMENT OF CHANGES IN BENEFICIAL OWNERSHIP

    Filed pursuant to Section 16(a) of the Securities Exchange Act of 1934,
       Section 17(a) of the Public Utility Holding Company Act of 1935 or
               Section 30(f) of the Investment Company Act of 1940

[_]  Check box if no longer  subject of Section 16. Form 4 or Form 5 obligations
     may continue. See Instruction 1(b).

________________________________________________________________________________
1.   Name and Address of Reporting Person*

Chellgren                               Paul                W.
- --------------------------------------------------------------------------------
   (Last)                           (First)             (Middle)

P.O. Box 391
- --------------------------------------------------------------------------------
                                    (Street)

Ashland                            Kentucky                41114
- --------------------------------------------------------------------------------
   (City)                           (State)              (Zip)


________________________________________________________________________________
2.   Issuer Name and Ticker or Trading Symbol

    Arch Coal, Inc. (ACI)
________________________________________________________________________________
3.   IRS Identification Number of Reporting Person, if an Entity (Voluntary)

________________________________________________________________________________
4.   Statement for Month/Year

     January, 1999
________________________________________________________________________________
5.   If Amendment, Date of Original (Month/Year)

================================================================================
6.   Relationship of Reporting Person to Issuer
     (Check all applicable)

     [X]  Director                             [_]  10% Owner
     [_]  Officer (give title below)           [_]  Other (specify below)
________________________________________________________________________________
7.   Individual or Joint/Group Filing (Check applicable line)

     [X]  Form filed by one Reporting Person
     [_]  Form filed by more than one Reporting Person
________________________________________________________________________________

================================================================================ Table I -- Non-Derivative Securities Acquired, Disposed of, or Beneficially Owned ================================================================================ 6. 4. 5. Owner- Securities Acquired (A) or Amount of ship 3. Disposed of (D) Securities Form: 7. Transaction (Instr. 3, 4 and 5) Beneficially Direct Nature of 2. Code ------------------------------- Owned at End (D) or Indirect 1. Transaction (Instr. 8) (A) of Month Indirect Beneficial Title of Security Date ------------ Amount or Price (Instr. 3 (I) Ownership (Instr. 3) (mm/dd/yy) Code V (D) and 4) (Instr.4) (Instr. 4) - ------------------------------------------------------------------------------------------------------------------------------------ Common Stock 1/27/99 P 3,000 A 12.9375 8,434(1) D - ------------------------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------------------------------ ==================================================================================================================================== (1) Includes 434 shares acquired pursuant to the issuer's dividend reinvestment plan. * If the Form is filed by more than one Reporting Person, see Instruction 4(b)(v). Reminder: Report on a separate line for each class of securities beneficially owned directly or indirectly. (Print or Type Responses) (Over) (Form 4-07/98)

FORM 4 (continued) Table II -- Derivative Securities Acquired, Disposed of, or Beneficially Owned (e.g., puts, calls, warrants, options, convertible securities) ================================================================================ 10. 9. Owner- Number ship of Form 2. Deriv- of Conver- 5. 7. ative Deriv- 11. sion Number of Title and Amount Secur- ative Nature or Derivative 6. of Underlying 8. ities Secur- of Exer- 4. Securities Date Securities Price Bene- ity: In- cise 3. Trans- Acquired (A) Exercisable and (Instr. 3 and 4) of ficially Direct direct Price Trans- action or Disposed Expiration Date ---------------- Deriv- Owned (D) or Bene- 1. of action Code of(D) (Month/Day/Year) Amount ative at End In- ficial Title of Deriv- Date (Instr. (Instr. 3, ---------------- or Secur- of direct Owner- Derivative ative (Month/ 8) 4 and 5) Date Expira- Number ity Month (I) ship Security Secur- Day/ ------ ------------ Exer- tion of (Instr. (Instr. (Instr. (Instr. (Instr. 3) ity Year) Code V (A) (D) cisable Date Title Shares 5) 4) 4) 4) - ------------------------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------------------------------ ==================================================================================================================================== Explanation of Responses: Miriam Rogers Singer February 5, 1999 - --------------------------------------------- ----------------------- **Signature of Reporting Person Date (Miriam Rogers Singer on behalf of Paul W. Chellgren) ** Intentional misstatements or omissions of facts constitute Federal Criminal Violations. See 18 U.S.C. 1001 and 15 U.S.C. 78ff(a). Note: File three copies of this Form, one of which must be manually signed. If space provided is insufficient, see Instruction 6 for procedure. Page 2