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	88	74	0	0.543	0.0
         Detroit	87	75	0	0.537	1.0
     Kansas City	82	80	0	0.506	6.0
       Minnesota	70	92	0	0.432	18.0
         Chicago	60	102	0	0.370	28.0
           Total	387	423	0

Chicago can finish the season with at most 60 + 0 = 60 wins and will finish the season behind the following teams:
Cleveland has already won 88 games.
Detroit has already won 87 games.
Kansas City has already won 82 games.
Minnesota has already won 70 games.
# Chicago White Sox' magic number
# Chicago's magic number
# White Sox' magic number
# MLB Playoff Race