Dr.Todd, I am in Illinois and fanny pack. This is transporting a handgun unloaded with a loaded magazine in the fanny pack or other container, also known as "6 seconds to safety"! I've been doing so for 8 years, using a black Uncle Mike's Sidekick Fannypack! Never been stopped by police when doing so. Out of staters can do this as well without a FOID card, since they are not eligible for one.
There should be no trouble flying in or out of Chicago with a handgun people do it all the time. We are Illinois, but not New Jersey. You can also conceal carry a loaded handgun concealed in your car if you are legal to do so in your own state. Just make sure it is unloaded (no round in chamber or magazine in gun) and cased if you go outside your car, say to put it in your trunk or to go in somewhere, the case must completely enclose the gun. It could be a fanny pack, purse, or other pack, brief case, luggage and it doesn't need to be locked. With a CCW from your state you are fine, and technically you probably are if you can open carry without one, though an Illinois LEO may not think so. Transportation laws in Illinois are fairly good and now uniform though the whole state. You can transport a handgun or other firearm unloaded and encased with a loaded magazine in the same case in the passenger compartment (6 seconds to safety) and the center console has been ruled to be a case by Illinois courts.
If you would like more input on this go to the Illinoiscarry.com forum, and post your question. There are a lot of knowledgeable folks there, especially the NRA lobbyist for Illinois , Todd Vandermyde!
If you have any questions on what I mentioned just ask and I'll clarify.