In the 50 and 60s the Sox and Cubs played an annual exhibition game usually in June or July, it was called the Boys Baseball Benefit Game. I've followed the Sox since the early 50s and this picture of the 1964 game is the largest crowd I've ever seen at Comiskey. I took my high school girlfriend to that game and as you can see fans were actually standing on the field from CF to the right field foul pole. We sat in an aisle and they were packed as well, there was no place to move in the park. The game was always played at Comiskey because they would draw more at night. If you look at the scoreboard the Cubs were the home team that night but the Sox creamed them like 11-4. Any ball hit into the fans on the field was a ground rule double. Open up the attachment to see the size of the crowd.
In the first half of the century the Sox and Cubs would play the City Series after the regular season, I believe it went on during the World Series. Some years it wasn't played since the Cubs made the World series a few times.
Here is a history of that Series. The Sox won most of the time.