Great question — answering as the UphillTech team:
For any reasonable definition of "near," no. However, if you hike into the more remote part of Indiana Dunes State Park and set up a tent, no one will bother you. I've done it with a group of 40. The rangers there are primarily concerned with people being drunk/loud in the designated camping area. This park has the advantage of being accessible by public transit (South Shore Line from Millenium Station). If you must stay compliant with park rules, your best bet is to drive north into WI. Nicolet National Forest is the closest good place I know, at 4.5 hours away. If you can tolerate a 7 hour drive, I recommend the Porcupine Mountains near Ontonagon, MI.
Full answer by Diogenes Creosote: https://outdoors.stackexchange.com/a/5680 (CC BY-SA 3.0).
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