This is a fun vintage piece that I assume is from the University of Tennessee. It is a wool felt with the "UT" applied. The hat was made and/or distributed by Staunton Novelty Co. of Staunton, Virginia. It is tagged as a 7 and it measures about 7 inches across though it is a shallow beanie vs. today's baseball caps.
The hat is in very good condition for its age. There are a couple of shallow spots from moths and the faux leather rim on the inside is dry and broken in places.