This weekend (June 22nd and 23rd), "When Radio Was" will feature an episode of "The Jack Benny Program" originally broadcast from Livermore, California in March of 1944.
The episode is being split into two parts: The first portion will be broadcast on Saturday (June 22nd); the remainder of the show will be heard on Sunday (June 23rd).
"When Radio Was" is nationally syndicated, and although I think Chicago's WBBM still broadcasts the show, I don't think they do so on weekends.
So check websites of radio stations in your area to see where and when you can hear it this weekend.