Rockefeller Memorial Chapel
I think that the Rockefeller Memorial Chapel is the most beautiful church in Chicago. The chapel fits 1,200+ people, and looks like a cathedral. It is in Hyde Park on the University of Chicago campus. From my understanding you must be somehow affiliated with the University to get married there.
The downside to getting married there is that you must do it only when school is not in session. This leaves the summer months and winter break. Also, it is not a religious facility, so if you are going to have a Catholic wedding, your officiant must bring everything to the site. The price for this place is steep, but worth the spectacular pictures you will have.
Rockefeller was the perfect location for our ceremony. They were great to work with, espcially in terms of the musicians. The chapel is a perfect backdrop for a romantic ceremony. Even though it is large, it still has an intimate feeling.
Beautiful vendor but beware -- you must do everything -- all you get is the venue. Be prepared to set-up chairs, take down decorations and be in and out exactly on-time. My maid of honor missed some essential photographs because the person in charge on our wedding day told her he was locking all of our belongings in his office if they weren't removed immediately at 4pm, the end of our wedding slot. He never showed us to the air conditioned rooms. Despite being told they could remove several large items blocking the view, on the wedding day they were not removed and the person in charge said they couldn't be moved. Despite being told there were enough microphones, there is only one. The officiant had to hold the wireless mic out to us as we repeated out vows. It is a true do-it-yourself venue. What a shame, because with a little bit of service it could have been a class act.