'Requiem for Methuselah' by Jerome Bixby

The crew of the U.S.S. Enterprise is struck down by the deadly plague Rigellian fever. In search of the only known antidote, Ryetalyn, Captain Kirk, Lieutenant Commander Spock and Doctor McCoy beam down to the supposedly uninhabited world of Holberg 917-G; but when the arrive on the planet they are surprised to meet a man named Flint and his daughter, Rayna. Flint is annoyed at the intrusion of the Starfleet officers, but agrees to order his robot to gather and process the Ryetalyn they need. However, the robot contaminates the first batch of the antidote, and so McCoy instructs it to make more; meanwhile, Kirk and Rayna fall in love, much to Flint's jealous objection. Spock is puzzled to discover a Leonardo da Vinci painting created with modern oils on a new canvas, and an unknown waltz by Brahms, written on new paper. Flint explains that he is an immortal; for centuries he wandered the Earth in various personas, including those of Brahms and da Vinci, but eventually decided to come to this planet to retire in peace. He built an android for a companion, and named her Rayna; unfortunately, Rayna's involvement with Kirk causes her to experience intense emotions, and she short-circuits and 'dies'...

William Shatner (Captain James Tiberius Kirk), Leonard Nimoy (First Officer Lieutenant Commander Spock), DeForest Kelley (Doctor Leonard H. ‘Bones’ McCoy), James Doohan (Chief Engineer Montgomery ‘Scotty’ Scott), Nichelle Nichols (Lieutenant Nyota Uhura), James Daly (Flint), Louise Sorel (Rayna Kapec)

Directed by Murray Golden

TX:
14th February, 1969

Notes:
*Featuring Captain James Tiberius Kirk, First Officer Lieutenant Commander Spock, Doctor Leonard H. ‘Bones’ McCoy, Chief Engineer Montgomery Scott and Lieutenant Nyota Uhura