Final answer:
The first Greek letter fraternity was Phi Beta Kappa, established on December 5, 1776, at the College of William and Mary by five students.
Step-by-step explanation:
The name of the first Greek letter society, commonly known as a fraternity, was Phi Beta Kappa. It was founded on December 5, 1776, at the College of William and Mary in Williamsburg, Virginia. The society was founded by five students at the college: John Heath, Thomas Smith, Richard Booker, Armistead Smith, and John Jones. It was founded by John Heath and some of his friends, who were rejected by the two Latin secret societies on campus.