I agree with AgRecruiter -- Vienna Beef or nothing, and Giordano's for deep dish pizza. Stuffed spinach pizza -- Good and good for you too! I'm not a big fan of Italian beef or gyros. Maybe not being from Chicago -- and living in the suburbs -- my opinion doesn't really count, but I think the best thing about food in Chicago is not one particular entree but the variety that's available. Also, like NYC, Chicago is large enough and has enough a) ethnic diversity, b) tourism, and c) businesspeople and others with $$ that there are many awesome restaurants.
If you are going to get a Chicago dog, make sure it says Vienna Beef. Anything else is rubbish. Giordano's for Deep Dish Pizza! Maxwell St. Polish sausage or try a trip to Portillo's for variety. I am pretty sure that Italian Beef is on the menu at any restaurant in Chicago. Gyros gotta be in Greektown near Halsted. I'm getting hungry! Thanks for making me want to move back to Chicago JPLovesCotton!