2267 (Columbia)

I.S.S. Enterprise (TOS 39)

January

Stardate Unknown: A transporter mishap slips Captain Kirk and his companions into a parallel universe, where the Enterprise serves a barbaric Empire instead of the Federation. (TOS 39: "Mirror, Mirror")
Stardate 3842.3: While transporting dignitaries to an important peace conference, the Enterprise is pursued by a mysterious vessel and an assassin is discovered among the passengers. (TOS 44: "Journey to Babel")
23 January/Stardate Unknown: Chapter 1 (VAN #5: "Precipice")

Stardate 4040.7: Captain Kirk and a landing party are forced to fight in gladiatorial games on a planet modeled after the Roman Empire. (TOS 43: "Bread and Circuses")
22-23 March/Stardate Unknown: Chapters 14-15 (VAN #5: "Precipice")

Stardate 4202.9: After losing his entire crew to an alien planet-eating machine, Commodore Matthew Decker pulls rank on Kirk in order to play a game of cat-and-mouse with the mechanical adversary. His efforts to destroy the menace place the Enterprise in grave danger. (TOS 35: "The Doomsday Machine")
Stardate 4211.4: Captain Kirk must decide how to save a primitive people from the technological interference of the Klingons. (TOS 45: "A Private Little War")
26-30 May/Stardate Unknown: Chapters 16-18 (VAN #5: "Precipice")

2-5 June/Stardate Unknown: Chapters 19-23 (VAN #5: "Precipice")
Stardate 4307.1: The crew of the Enterprise encounters an energy-draining space creature. (TOS 48: "The Immunity Syndrome")

Stardate 4372.5: Captain Kirk hosts a spoiled princess, who must bring peace to a star system at war. (TOS 57: "Elaan of Troyius")
Stardate 4385.3: For trespassing on an alien world, Captain Kirk and his companions are forced to re-enact the famous shoot-out at the O.K. Corral with themselves cast as the losing side. (TOS 56: "Spectre of the Gun")
14-21 July/Stardate Unknown: Chapters 24-26 (VAN #5: "Precipice")
30-31 July/Stardate Unknown: Chapters 27-29 (VAN #5: "Precipice")

Stardate 4513.3: Captain Kirk and the crew have another run-in with Harry Mudd, this time finding him as the king of a planet of androids. (TOS 41: "I, Mudd")
9-10 September/Stardate Unknown: Chapters 37-49 (VAN #5: "Precipice")
12-14 September/Stardate Unknown: Chapters 50-52 (VAN #5: "Precipice")
Stardate 4523.3: Tribbles—purring, limbless, and fertile—disrupt the colonization of a disputed planet between the Klingon Empire and the Federation. (TOS 42: "The Trouble With Tribbles")

Stardate 4598.0: The Enterprise visits a planet with a violent culture based on America's 1920s prohibition era. (TOS 49: "A Piece of the Action")
Stardate 4657.5: Beings from the Andromeda galaxy steal the Enterprise, modify it, and attempt to return home. (TOS 50: "By Any Other Name")
Stardate Unknown: Captain Kirk must battle a deadly virus and a treacherous fellow starship captain to stop an intertribal war. (TOS 54: "The Omega Glory")
Stardate 4729.4: A new computer system causes havoc while being tested aboard the Enterprise. (TOS 53: "The Ultimate Computer")

Stardate 4768.3: Telepathic aliens take control of Kirk and Spock's bodies with the intention to build new, mechanized bodies for themselves. (TOS 51: "Return to Tomorrow")
Stardate Unknown: During an historical research mission in 1968, the Enterprise encounters Gary Seven, a human with advanced technology who appears to be attempting to alter Earth's history. (TOS 55: "Assignment: Earth")
28-29 December/Stardate Unknown: Chapters 54-60 (VAN #5: "Precipice")
Stardate 4842.6: A mysterious alien device on a planet with a predominantly Native American culture erases Captain Kirk's memory, and he begins a life with them as a member of their tribe. (TOS 58: "The Paradise Syndrome")