There are 3 that I know of.
Chestnut Mountain: Probably the best one in Illinois proper. Small but on par with anything else in southern Wisconsin except Devil's Head or Cascade.
Villa Olivia: Close to Chicago, very small and not worth the money for the lift ticket. Lots of parents drop off there kids there for the day, so there's that to deal with also.
Four Lakes: Exceptionally small as well. I have never been there but I had a few fiends that used to go there just to mess around in the terrain park.
Wilmot Mountain: This one is actually just on the other side of the border so I suppose it doesn't count but it's definitely one of the better "close-by" options if you live in Chicagoland.
I agree with Slyder though, you are better off looking at places in Wisconsin. Alpine valley is OK if you are looking for something a little closer to Chicago. Otherwise, either Cascade or Devil's head would be pretty good for a day trip if you don't mind driving a little more. If you're doing an overnight trip check out Granite Peak or anything in the UP.