Having gardened in places much colder than Chicago :-), my guess is that it would overwinter just fine in a container. Peonies are very tough and cold hardy. If you are still worried, move it to a sheltered place, like a shed or garage or wrap the pot in some bubble wrap and put it under your eave.

My peonies survive just fine here, and I'm 800 miles further north than you are. they get no special protection. i even grow Japanese tree peonies here, and they do fine as well.

I have 3 lovely peonies I didn't expect to move in my lifetime, yet found a new place we couldn't pass up. The problem: We are trying to sell our existing home now (no takers so far), but the new house won't be ready to move into until probably next September. I have already cut the peonies back for the season. Should I/can I dig them up & keep in the refrigerator, and how do I prepare them for that? Would that be OK till next fall? Doing so, they would miss out on an entire growing season! Should I replant someplace safe on the new property, then plan to move again when I know where I want to put them? (this doesn't seem like a good idea). Or do I (very sadly) leave them where they are, for the enjoyment of others? I realize if I choose either of the first 2 options, I'm not likely to see blossoms for a very long while...

I would pot them up and sink the pot in the soil of the new location. They will survive in good condition and can be moved easily when you are ready for their permanent planting. Al