When talking about Greek Life, colleges usually talk about fraternities and sororities. However, BYU does not have any sororities or fraternities. According to the 100 Hour Board, "...many people of a certain social class belong to fraternities and sororities, but you might as well say that having a beard makes you a better military leader because most of the Civil War generals had one." Thus, BYU disallows Fraternities, Sororities, and Greek life in general (byu.edu).
BYU used to have one fraternity, Lambda Delta Sigma, but it was replaced by the LDS Student Association (byu.edu).