I used to live in the Windy City, but things change so the venues I'm naming could be defunct by now.
Green Mill on Broadway
Green Dolphin Street on Ashland
Elbo Room on Lincoln Ave
Fitzgerald's in Berwyn
Cotton Club on Michigan Ave
Andys off of Hubbard
Check out the Chicago Reader or the Illinois Entertainer and look up the Jazz clubs listed there. That would be a great place to start. The weekend section of the Tribune or Times is a good resource as well.
Also, look outside the club scene. Since you're playing Jazz you'll have in roads where many rock bands won't. Take a look into some of the swanky hotels in the area and see if you could perform there for an event. Give a call to the various event and wedding planners in the area. Try calling some of the cultural associations to see if they are sponsoring any performances. They might be able to get you into a gig at a museum or other event that will get your band great exposure.
Hope this helps.