The Burger Bar Chicago can make any of their burgers on a gluten-free bun. The employees told us that they take allergies very seriously, which was reassuring.
You can order set burgers off the menu or you can make your own. On Saturday evening August 1, 2015 mine came out perfectly with everything on it that I wanted. The bun was so good, I would not have guessed it was gluten-free. Also, the burger was cooked just they way I wanted, medium rare. The Samoa milk shake was very good as well.