To add to my post:
While I've only been there once, Hard Knox is really good in Knoxville. Not much of a chain as I think they only have 2 locations, but very good pizza.
Giordano's Chicago Style is probably the best pizza I've ever had. It's a staple if Chicago, but only a couple locations outside of Chicago. I've been to the one in Orlando. BBQ chicken pizza is off the charts. There's at least 2 locations in Chatt. Not sure about Knoxville.
Old Chicago is a sit down restaurant chain, a little similar in theme to Buffalo Wild Wings. It's a Midwestern chain based out of Colorado I believe, with about 80 locations nationwide. They have good quality Chicago style pizza too. Nothing that's gonna knock your socks off, but considering the pizza options in TN, they are certainly one of the best. Great wings and beer too.
If you're in Chattanooga, Community Pie is by far the best I've found. Locally owned, they have both Neopolitan and NY style pizza. Fresh ingredients and some very unique toppings.