Where No Man Has Gone Before - S1-E4
Trivia: This was the second pilot for the series, the first pilot being done with Jeffrey Hunter as Capt. Christopher Pike. This is also the first episode that has William Shatner as the famous Capt. James T. Kirk. The episode was made at the request of Lucille Ball, part owner of Desilu Studios, and friend to Gene Roddenberry, because she believed in the franchise.