The Chatham County Historic Courthouse stands in the middle of Pittsboro's downtown roundabout, giving the town its shape and most of its old-courthouse character. Built in 1881 and restored after a 2010 fire, it now houses the Chatham Historical Museum.
The museum is small, but the building and square are worth a look even if you do not go inside. It is the natural starting point for a walk through downtown Pittsboro.