Funny you should say that...just this week I wrote a love letter to Chicago pizza...
It figures a Texan would like it. It was popularized, and some say invented by, a Texan who liked the Italian ingredients but wanted something more like what folks at home would eat.
[I know there's a dispute about whether Ike Sewell came up with it in his kitchen or, more likely, teamed up with /stole it from someone else who came up with it, but certainly Uno's became associated with it and even helped popularize the style outside Chicago]
Not having chased the stuff down during a visit to Chicago, I can't really opine on the best deep dish, but I'm sure it is enjoyable. I like what passes as deep dish at the Uno's chain, and I will guess there's much better stuff out there. Just don't call it pizza. To me, it is like saying roast chicken and fried chicken are the same dish.