Sorry, the summer quarter IS the fourth. So the normal school year is three quarters with summer being the fourth. So in the fall, they start a bit later than other schools do. You can see their current schedule here: http://www.uchicago.edu/academics/calendar/

I only know this cause my best friend and my HS boyfriend both went there for undergrad (many, many years ago).

I've been organizing a lot of Supernatural info since I watched, and the one thing I realized is this show has absolutely no regard for any timeline. Bah!