Fly into somewhere else...
What's with the bashing of Chicago, it's no different than any other state. Follow the guidelines of TSA and the airlines.
I think the problem occurs when you leave the airport and head off into town with the firearms. That's what I read here, not saying I understand the gun laws in Chicago.
The gun laws of ILLINOIS are the governing body. The only thing in Chicago is you can no longer register a handgun in the city of Chicago. As far as the packaging, and the transportation of your firearms, they are basically the same as when your traveling on an airplane. (Gun Case,ammo seperate from firearm) If in doubt, go tho the Illinois State Police home page for all the rules.
Don't get perinoid !