There's gotta be someone in chicago. You could try calling any of the commercial studios in Chicago and do one of two things. Sometimes studios will do this:
1) Ask the studio if they have an option to rent out some of thier in-house mics and work out the deal (usually with the studio manager).
or
2) Ask the studio if they could extend you the number of any of their equipment rental networks in the area.
Even commercial studios have to "outsource" sometimes when they need to rent specific types of gear, therefore, there should be shops setup close by to service that need. These shops can be pretty hard to find, so you might get lucky talking to one of the local production houses.
If not, I know there's a company abased in NY that specializes in gear rentals as a mail order system. It might be worth looking into:
www.dreamhire.com
I'm hoping your pockets are deep for the kind of stuff you're looking for.