The only two airlines I know of in the Chicago area are United (I suppose that one is obvious) but they are not hiring at the moment and require a couple of years experience dispatching before you can get hired, even if they were. The other carrier I know of is Ryan International Airlines, based in Rockford, IL. They likely would prefer some experience as well, although less than United. I don't know a lot about them; they so subservice contracts, cargo flights, etc. Not sure if they are hiring right now or not.
If you're willing to go a bit further afield, Air Wisconsin is based in Appleton, WI, about 180 miles north of Chicago. I have heard they are looking for a new hire dispatcher right now, and they have been known to hire people right out of school. However, Air Wisconsin no longer flies into Appleton, so getting there for an interview you'd have to drive up from Milwaukee most likely.
There may be other operators in the Chicagoland area, but those are the ones I know of. Sometimes ground handling companies will hire dispatchers at a big international airport like Chicago to do the paperwork and weight/balance stuff for international airlines that fly there, but it's not something I've ever researched in any detail.
