My favorite is Michele's Chicago Pizza on Walsingham in Largo (Corner of Ridge and Walsingham-across from 7-11). If you are going, go on her website and check out the mapquest, because there are two Ridge's and two sections of Walsingham as well. http://micheleschicagopizza.com/
They have four styles of Pizza. From thinnest to thickest: Chicago Thin Crust, Thick Crust,
Pizza in the Pan (kind of like Gino's Style), and Stuffed Pizza (kind of like Giordano's Style).
The two thicker styles are really thick. Each Pizza weighs several pounds. A very fussy food snob I know (kind of like me) really enjoyed it, when he visited from Miami, declaring it authentic Chicago Deep Dish Pizza.
They also make really good wings. I haven't been out there in a while, but now I need to go soon.
re: Robert R
I second Michele's as being the best deep dish you can get in Pinellas. Don't let the sort of sketchy strip mall appearance dissuade you from going. It's the real deal. Also keep in mind that there really isn't any seating to dine in, it's best enjoyed as take-out.
A second option for deep dish that isn't nearly as authentic is BJ's Brewhouse in Pinellas Park.
I third Michele's (her thin crust is great, too), and also recommend Untouchables Pasta and Pizza - 1150 Clearwater Largo Rd N in Largo. Slightly sweet sauce (I like how it counteracts the acidity), and fresh toppings. Being originally from Chicago, I appreciate their use of real sausage vs. the "bunny bits" you get on many pizzas down here.