An oath of celibacy was a promise that Deltans were obligated to swear to upon service in Starfleet, stating that they would not take advantage of any of their non-Deltan crewmates. This was necessary because Deltans were a highly sexualized species and viewed Humans as immature in this regard.

Ilia filed her oath of celibacy before commencing her duties aboard the USS Enterprise. (Star Trek: The Motion Picture)