funny, I've never heard of them, and we have 4 Middle Eastern restaurants within 6 blocks of my house - plus another 2 Greek places! We have shish kebabs and kefta kebabs and wraps and shawarma and gyros and lots of other stuff, but no doner kebabs!
But I did find a "Doner kebabs in Chicago" thread on a random message board https://www.roadfood.com/Forums/Doner-Kebabs-in-Chicago-m676557.aspx
same thang