Chicago has been eliminated from first place.

To show that Chicago is eliminated from first place, we start with the current standings:
            Team	W	L	GL	PCT	GB
         Detroit	85	66	11	0.563	0.0
       Cleveland	79	71	12	0.527	5.5
     Kansas City	75	76	11	0.497	10.0
       Minnesota	66	85	11	0.437	19.0
         Chicago	57	95	10	0.375	28.5
           Total	362	393	55

Chicago can finish the season with at most 57 + 10 = 67 wins and will finish the season behind the following teams:
Detroit has already won 85 games.
Cleveland has already won 79 games.
Kansas City has already won 75 games.
# Chicago White Sox' magic number
# Chicago's magic number
# White Sox' magic number
# MLB Playoff Race