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
       Cleveland	92	69	1	0.571	0.0
         Detroit	86	76	0	0.531	6.5
     Kansas City	86	76	0	0.531	6.5
       Minnesota	82	80	0	0.506	10.5
         Chicago	41	121	0	0.253	51.5
           Total	387	422	1

Chicago can finish the season with at most 41 + 0 = 41 wins and will finish the season behind the following teams:
Cleveland has already won 92 games.
Detroit has already won 86 games.
Kansas City has already won 86 games.
Minnesota has already won 82 games.
# Chicago White Sox' magic number
# Chicago's magic number
# White Sox' magic number
# MLB Playoff Race