Chicago White Sox First-Place Eliminiation Scenario
Chicago must win 0 more games (63 total) to avoid elimination from first place.
Here is a scenario in which Chicago can finish in first place with 63 wins.

To construct the scenario, we start with the current standings in the division:
Team             W	L	GL	PCT	GB
Chicago          63	45	54	0.583	0.0
Cleveland        52	53	57	0.495	9.5
Detroit          52	58	52	0.473	12.0
Kansas City      46	60	56	0.434	16.0
Minnesota        45	63	54	0.417	18.0

Next, we show how the remaining series of games plays out in the scenario:

Chicago wins 0 games against Cleveland and loses 5.
Chicago wins 0 games against Detroit and loses 6.
Chicago wins 0 games against Kansas City and loses 4.
Chicago wins 0 games against Minnesota and loses 3.
Chicago wins 0 games agains teams outside the division and loses 0.

Cleveland wins 5 games against Chicago and loses 0.
Cleveland wins 4 games against Detroit and loses 2.
Cleveland wins 2 games against Kansas City and loses 8.
Cleveland wins 0 games against Minnesota and loses 10.
Cleveland wins 0 games agains teams outside the division and loses 0.

Detroit wins 6 games against Chicago and loses 0.
Detroit wins 2 games against Cleveland and loses 4.
Detroit wins 3 games against Kansas City and loses 0.
Detroit wins 0 games against Minnesota and loses 4.
Detroit wins 0 games agains teams outside the division and loses 0.

Kansas City wins 4 games against Chicago and loses 0.
Kansas City wins 8 games against Cleveland and loses 2.
Kansas City wins 0 games against Detroit and loses 3.
Kansas City wins 5 games against Minnesota and loses 1.
Kansas City wins 0 games agains teams outside the division and loses 0.

Minnesota wins 3 games against Chicago and loses 0.
Minnesota wins 10 games against Cleveland and loses 0.
Minnesota wins 4 games against Detroit and loses 0.
Minnesota wins 1 games against Kansas City and loses 5.
Minnesota wins 0 games agains teams outside the division and loses 0.

Combining the current standings with the wins and losses from the scenario results in the following final standings:
Team             W	L	PCT	GB
Chicago          63	99	0.389	0.0
Cleveland        63	99	0.389	0.0
Detroit          63	99	0.389	0.0
Kansas City      63	99	0.389	0.0
Minnesota        63	99	0.389	0.0