The Harold Washington Library in downtown Chicago has an excellent archival collection of production information, photos, old stagebills, and other material pertaining to Chicago theatre history.
The website has some information about what you will find there--Archival Collections--Theater. There's also a limited amount of digitized content--Digital Collections--Theater.
The Chicago Theater History Project--maintained by Columbia College--there's a good bibliography here.
Try doing a Google search to dig out other potentially useful web sources--don't forget to check credibility!
The Newberry Library has many resources on Chicago theatre history. You can search their catalog here--Newberry catalog If you find something there that inspires, you can make an appointment to do research at the Newberry itself, ask Peg for info on how to do this.