I agree with the lot. You will most likely not need chains. I lived in Chicago most of my life and I never chained up once. Unless you plan on climbing hills on some unmaintained back country roads, I think you will be fine. Being that most of the terrain is flat, I highly doubt you will have any trouble getting around. That's not to say you need to drive safe in these conditions, but you should be fine with the Axy.
The only time I have ever used chains was out here. I once drove over the pass (from Reno to Sacramento) in the middle of a blizzard with a rental car. Chains were required for all non-4x4 vehicles. So I went to Wally World and got the cheapest chains I could find. Let me just say, putting them on was NOT fun. They work, but they are a serious pain in the bootie.
Bart