Pirate:
If your location truly is "Chicago, IL" then the answer is NO.
Elsewheres (where possession of handguns is lawful), you are within the law to do so.
But I live in a very residential area, still in Cook county. So, for example, I went about mowing my lawn open carry, while it would be lawful to do so, nosey and worried neighbors would likely call my local PD. Knowing some of them as I do, I suspect they would just smile and say "we'll try to calm your poor neighbor down." Yet it could turn out that they might tell you to put it away, as you are "causing public alarm" or "being a public nuisance."
That is just the way it is in gun-unfriendly locations. What's lawful isn't the same as what is acceptable.