Final answer:
Alpha Phi Alpha, the first black fraternity, was established at Cornell University, not an HBCU but a predominantly black institution during the time of its founding.
Step-by-step explanation:
The first black fraternity, Alpha Phi Alpha, was established at the predominantly black institution, Cornell University, despite Cornell's not being a historically black college or university (HBCU). This historic event took place during a period when African American students were seeking to create communities and support networks within predominantly white institutions.
The National Pan-Hellenic Council, which oversees nine International Greek letter fraternities and sororities, includes this fraternity among its ranks.