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#58: Star Trek: The Original Series, season 3, episode 3 "The Paradise Syndrome"
Written by Margaret Armen, directed by Jud Taylor.
Stardates 4842.6 through 4843.6 (September 2268)
"Surely no man has ever attained such happiness." - Kirok
The Enterprise finds a planet within the path of an asteroid that has evolved to almost exactly resemble the ancient Americas on Earth. Additionally, they find a nomadic people who resemble some of the Native American tribes. Only a strange obelisk of unknown design suggests that an advanced people had once been there. Opting to leave the natives alone and focus on the asteroid, Captain Kirk, Commander Spock, and Doctor McCoy prepare to return to the ship. Upon contacting the Enterprise, Kirk accidentally activates an entrance hatch to the obelisk and falls in. Inside, he fumbles around and touches the advanced controls causing his memory to be wiped. Outside, Spock and McCoy, unable to locate the Captain, return to the ship in order to intercept the asteroid in time. Kirk is found by one of the nomadic natives and taken in. He is believed by the elders to be the fulfillment of an ancient prophesy that tells of a god who will appear to the people during a time of great need. As Spock and the crew use all of the Enterprise's strength to keep the asteroid from striking the planet and killing everyone on it, Kirk slowly believes he is the one the prophecy spoke of and begins a new life filled with a simplicity and peace he's never known before.
Originally released: 4 October 1968
"The Paradise Syndrome" on Memory Alpha (mirror)
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What did you think?

At least the asteroid doesn't look like a wad of foam anymore.