I have been out in California 8 years now. Take lots of visitors to In & Out as part of their LA visit experience (because they want to go). That is about the only time I make a visit. Just don't get the hype.

You now have The Counter in Chicago -- have you tried that yet? Plus you have a Fatburger in Chicago too. I may be a little partial to The Counter because the original one is down the street from me here in Santa Monica. But would take a visit there or Fatburger any day over In & Out or Five Guys. Not similar per se - just better.

In answering the original question, the best bet would probably be a friend buying one at the In & Out in Grapevine, Texas on the way to DFW. It could probably be to Chicago and in your mouth in 3 hours if the security and weather gods align and you meet your delivery at ORD.