It's not illegal for a resident to own a handgun.... the problem is that you cannot legally possess it within city limits. Both airports, O'Hare and Midway are within city limits.
I don't get Illinois law.
A resident of Chicago can own, but not possess within the city, a handgun? Who issues the permits? I would assume it would be some agency within the city, how do you convince them that you won't bring the gun into the city? Most people don't have two houses. Where are you supposed to leave the thing?
Anyway, technically, I believe that the federal law would protect you. For instance, you own a handgun and have a permit and keep it stored in you beach house outside Chicago. You are headed to FL (or some such place where you have a permit and/or your gun is legal) and you intend to fly from O'Hare. Your gun is "legal" on both ends of the trip. If it is properly cased and declared then, again technically, you would be fine.
In the real world of Chicago, um, NO, don't do it.
Still happily answering to the call-sign Peetza.
The problem, as you so eloquently put it, is choice.
He is no fool who gives what he can not keep to gain what he can not lose.
-Jim Eliott, paraphrasing Philip Henry.