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 in the 2270s. She formally stated this to Captain James T. Kirk upon boarding, and he gave her permission to continue. (Star Trek: The Motion Picture)