WARNING: This thread WILL contain unhidden spoilers for this entry. Because this re-watch is in a slightly-subjective chronological order and not in production order, please refrain from talking about the content of other episodes or movies in this thread. If you do, please put that content inside spoiler tags. Some people here may be watching Star Trek for the first time.
#23: Star Trek: The Original Series, season 1, episode 28 "The City on the Edge of Forever"
Written by Harlan Ellison, directed by Joseph Pevney.
Stardate unknown (October 2267)
(Some events take place during January ~ March 1930)
"She was right, but at the wrong time." - Commander Spock
The Enterprise is being rocked by waves of temporal displacement emanating from a planet when Doctor McCoy accidentally injects himself with a dangerous stimulant. He goes mad and runs amok through the ship, ultimately beaming down to the planet right in the middle of a very large displacement wave. Captain Kirk, Commander Spock, and several others follow him down to the planet and discover a sentient gateway through time that offers them a chance to travel to any point in their past. McCoy sneaks past them while they are distracted and leaps through the portal to Earth's 20th century. The Enterprise vanishes and the gateway informs them that their entire Federation has never existed because of something McCoy did in the past. Kirk and Spock are left with no other choice but leap as closely to where McCoy went in the hopes of undoing the damage.
Originally released: 6 April 1967
"The City on the Edge of Forever" on Memory Alpha
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What did you think?

You mean "Battle Bridge Conn" then "Security Guard 1" then "Transporter Chief"? And not until "Unnatural Selection" partway through SEASON 2 is he finally Chief Miles O'Brien. Gets no respect, I tell ya.