Hands down, Bocci makes the best Chicago-style deep-dish pizza in the Raleigh, Durham, Chapel Hill area!
You'll need to swing by Hemlock Bluffs park afterward to walk off these calories though.
Maybe not quite as awesome and authentic as you'll find in Chicago, but their pizza will surely satisfy your craving.
Their smallest, the 12", should easily feed 4 hungry people.
We two, however, only made a dent in it tonight:
Bocci has plenty of other excellent Italian dishes, too, but we always order the Chicago pizza since no other restaurants in the area make one. It's easy to order vegetarian here, but to eat purely vegan might be a bit of a challenge.
From the location and ambience, you might think this would be an expensive restaurant, but not so. Bocci is casual, comfortable, and an excellent value-for-the-money no matter how you measure it.
Two thumbs up, as always!