Shore Leave - S1-E16
Trivia: William Shatner recalls having a "lame-brained" attack of bravado during "Shore Leave's" filming and insisting that Kirk should wrestle the tiger - without a stunt double. Gene Roddenberry finally convinced him that he was much too valuable to the show to risk his life for a stunt. Thirty years later on a Sci Fi Channel special, Shatner said, "Thank you, Gene, for preventing me from becoming a hair ball!"