Palos Forest Preserve is pretty much the only real mountain biking in the Chicago area. If you are up there for any reason, it's worth taking some time to slip a ride in while you are there. It's located on the south side and has plenty of good swoopy singletrack and even some DH features. You'll see weekend warriors and people with full face helmets because there is a wide variety of trail to ride there. Local bike rentals are close enough that you can rent bikes and literally ride to the trail head.
Location: Willow Springs, IL
Directions: Take I-294 South and exit at 75th Street towards Willow Springs Road. Take Willow Springs Road south to 95th Street. At 95th, head west to the Maple Lake East trail head.
Trails: Because this is Chicago do not expect any large climbs or big downhills. There are plenty of smooth, swoopy trails so you can ride it fast. There are downhill areas that feature jumps and drops, so there is a playground of sorts for those of you into the harsher riding. Trails are well marked with good signage throughout.