I know the question was about thin crust, but I'd like to put in a word for Calo's stuffed pizza too-- it's not too cheesy or too greasy, the sauce is tangy and the crust has a nice cornmeal crispness to it that I like. (Admittedly, I've never had it delivered, so I don't know how well it holds up in transit). And, like everyone else says, their thin crust is excellent.
There's a couple of places halfway between Andersonville and Lincoln Square that might deliver:
-- Pizzeria Bubamara, which has a charismatic eastern-European owner and a wide and strange assortment of toppings, gets people's attention with, like, cherry & crab meat pizza, but their ordinary no-funny-business thin crust is very good.
-- Stefano's, which is really a Giordano's, or was formerly a Giordano's, or will soon be a Giordano's, delivers to Andersonville. So, if you like pizza that is/tastes-exactly-like Giordano's, there's Stefano's.
-- Leona's delivers to Andersonville, if you like Leona's (I don't remember if it's the Sheffield or the Sheridan location).
Pizzeria Bubamara
4607 N. Wolcott
(773) 334-2633
Stefano's
2124 W. Lawrence Ave.
(773) 271-9696
http://www.stefanosstuffedpizza.com
(not to be confused with
http://www.stefanospizza.com, which is, strangely, a Chicago-style pizza place in Knoxville, TN)
Leona's
6935 N. Sheridan
(773) 764-5757
or
3215 N. Sheffield
(773) 327-8861
http://www.leonas.com