Kappa Alpha Theta has the oldest founding chapter continually in existence... (Phi Mu, Alpha Delta Pi and Pi Beta Phi's founding/Alpha chapters have all been closed at one point.)
BUT
Pi Phi has the oldest continually running NPC chapter, Iowa Alpha. (Drat them
)
And yes, Theta is "the first greek-letter fraternity known among women." The letters
KAQ were a symbol of the fraternity from the beginning in 1870.
Alpha Phi is close though.