Tau Kappa Epsilon - Beta chapter is the oldest (and best) Fraternity on Millikin's campus celebrating 100 years just a few days ago.

At Ole Miss the oldest frat on campus is DKE, but the oldest frat still on campus is Beta Theta Pi.

Actually, there are at least two that were founded before Beta at Ole Miss. Beta’s Beta Beta chapter was founded in 1879. Phi Kappa Psi and Sigma Chi (two that come to mind) were founded in 1857 I'm pretty sure. If you meant continuously open that wouldn't work either because Beta was off-campus for a while, and just about all fraternities left in the 1920s because fraternities and sororities were banned for a few years by the State Legislature.

Penn State Behrend.

The oldest fraternity of record at University of Mississippi was called WWW Rainbow, founded in 1849, DKE followed in 1850. All chapters closed during the Civil War. The Rainbow group revived in 1867 and the entire national was absorbed by Delta Tau Delta in 1866 (thus, the title of the Delt magazine). Beta was a relative latecomer in 1879.

Indiana University-
Frat: Beta Theta Pi (Pi Chapter)
Sorority: Kappa Alpha Theta (Beta Chapter)

Johns Hopkins University
 

Johns Hopkins was founded in 1876. Beta Theta Pi, Alpha Chi chapter, was founded in 1877. They're the oldest, but Phi Kappa Psi was close behind in 1879. I don't think either has ever closed/recolonized.

JHU didn't start admitting women until 1970, and in 1982 both Phi Mu and Alpha Phi colonized, making them the oldest sororities on campus. I believe Alpha Phi was recolonized at least once though, so I would say Phi Mu is the oldest continuously running sorority.

George Mason University
 

If I remember correctly a local was colonized by Kappa Sigma and that colony helped start a local sorority that later became Chi Omega, which I think is funny because a Kappa Sigma was one of the founders of Chi Omega.