Natural background radiation in Chicago
(all numbers per year)
26 mrem for cosmic radiation
2 mrem for elevations up to 1000ft
46 mrem from terrestrial K, U, Th in soil (aka not Colorado Plateau or Gulf and Atlantic Coasts but normal US soil)
0 mrem from radon&daughter products (I'm excluding it here from this calculation but it's a sizeable percentage of your yearly dose)
74 mrem total, which comes out to about 8.4 urem/hr or microrems per hour. The long-term average in my basement office runs at about 7.6uR/hr.
From Duval, J.S., Aerial gamma-ray surveys of the conterminous United States and Alaska, you can see here that the approximate average exposure rate from naturally occurring U, K, and Th in the ground is about 4.5uR/hr at 1m above the ground for Chicago. I say about because the survey didn't look at heavily urbanized ground. But with the high resolution data and a geologic map you should be able to predict what it should be.
The Straight Dope unfortunately printed an error about it in 1980, claiming the rate in Chicago was 2 millirems per hour. That's really off; it's 1/250 of that.