I saw that someone mentioned Gamma Sig...
My sorority is turning 50 in about 4 days
and we have quite a few chapters Nationally. However, we are not recognized by PHC because not only are we a service sorority, but because our sorority has a "non-selectivity" policy. This would make it impossible to participate in PHC Rush activities.
At some schools though, GSS chapters have to affiliate with a Greek Council in order to function on that campus at all. In those cases, it's okay. However, that chapter knows that anyone is welcome to join the chapter without the chapter being selective.