When those of us not native to the Windy City think of Chicago-style pizza, the first (and perhaps only) one that springs to mind is deep-dish. As it turns out, though, there are three types in all.

Chicago is home to iconic foods like Italian beef, deep-dish pizza and hot dogs, but it is also the birthplace of many well-known chain restaurants.

Any way you slice it, the Chicago pizza market is intense, but that’s not stopping the folks at Nancy’s Pizza, a McKinley Park, Ill.-based carryout and delivery concept, from pursuing growth. Founded ...