Isn't it just like me to throw a monkey wrench into this question? I thought the University of Pennsylvania was first. If it's not Penn, I'll go for William and Mary.
Well, Gloria, it may have been the University of Pennsylvania but my source says.. ha...Harvard...here's some more: (and thanks!)
Started in 1636 as an all-male school to educate Puritan ministers, this college had only nine students and one teacher. Today it has grown in enrollment to 18,000 undergraduate and graduate degree candidates and has become perhaps the best known educational institution in the world.