Please check with all the airlines you intend to travel with for their policies on traveling with guns. Also, check to see if they declare that you are carrying firearms if they land at different cities along the way. There are states, and cities, that will confiscate your guns because you are not a resident of that state/city whether you are legal in your state or not. New York is one such state, as is neu joisey and although I am not sure about chicago, I would bet my guns on being able to get out of the airport with my baggage and not be arrested.
I had a friend whose Dad gave him a WWII Walther he brought back - it was registered and licensed. My buddy licensed it in Colorado where he lives and checked with the NY State authorities who said it was ok to fly with it to Colorado. However, the plane stopped in Newark, the pilot stated that a passanger had a gun in his luggage, he was taken off the plane, arrested, the gun confiscated and it cost him 2 grand to get out of it and he lost the pistol - which is now probably riding in some NJ cop's back pocket.
Don't lose your guns to misinformation. Mikey.