So, I could be heading out to AZ soon, Phoenix specifically.  I obtained my AZ CCW when I lived there and because it is a free state I can CCW when I visit and with the kidnappings and all that would probably be a good idea.  Hell, I could even take my AK with me and have it ride in the passenger seat if wanted to.  

I am currently an IL resident, live in a "non-restrictive" county and city, and thankfully I finally received my FOID card.  I want to take my Glock 19 with me on my visit and I own "high" capacity mags, so can I transport and check these at either airport?  I realize that there are laws forbidding the ownership and possession of just about everything in Cook Country, but what about travelers?  I'm no stranger to checking firearms at airports, but I have never done this at MDW or ORD.

Please advise and/or send me some links to info.

Thanks.

I've never dealt with the TSA at Midway, but I have flown out of O'Hare a few times with pistols and never has any problems. I assume you are familiar with the ammo packaging requirements. A friend had his ziplock with loose ammo confiscated a while ago.

I've checked rifles through at O'Hare with no problems.  Be advised that O'Hare has a reputation for "losing" checked pistols, particularly if you fly United.  
http://www.redorbit.com/news/business/615582/gun_thefts_reported_at_ohare_airport/index.html
http://www.thefiringline.com/forums/showthread.php?t=219184


Traveling to and from Midway can be tricker as you will be in Chicago's city limits for a good stretch.  If you are pulled over and your weapon/magazines found, technically they would have a cause to confiscate them and arrest you.  FOPA states in part:

"Notwithstanding any state or local law, a person shall be entitled to transport a firearm from any place where he may lawfully possess and transport such firearm to any other place where he may lawfully possess and transport such firearm if the firearm is unloaded and in the trunk. In vehicles without a trunk, the unloaded firearm shall be in a locked container other than the glove compartment or console."
http://www.nraila.org/GunLaws/Federal/Read.aspx?id=60
http://en.wikipedia.org/wiki/Firearm_Owners_Protection_Act

Being an IL resident complicates things.  FOPA applies to interstate travel, not intrastate. I think the argument would have to be that your destination is not the airport, but whatever city and state you are flying to.