Out in the reaches of space, the Federation starship Reliant is looking for a dead planet to test the wondrous Genesis Device on.
Ceti Alpha Six looks like a good fit, but there's some weird readings on the Weird Readings O-Meter.
After hurriedly checking with Dr. Marcus (Bibi Besch) on space station Regular One to make sure it's okay, Captain Terrell (Paul Winfield) and Commander Chekov (Walter Koenig) beam down to check out the weird readings.
After the call, Dr. Marcus's son David (Merritt Butrick) opines that the Genesis Device could become an awful weapon if the wrong people got ahold of it.
Hmm: could this be foreshadowing? (Answer: yes.)
Chekov and Terrell beam down, only to find the ruins of an old ship, the Botany Bay.
Chekov promptly freaks the heck out and tries to split, but they're caught by the surviving crew of the Botany Bay. It's led by Khan (Ricardo Montalban), owner of the most imperious pectoral muscles in the whole universe.
Exposition time: Khan explains how James T. Kirk exiled him and his crew there fifteen years ago, after Khan kinda-sorta tried to kill him and hijack the Enterprise.
Starfleet thought the planet was Ceti Alpha Six; turns out, it's Ceti Alpha Five, which was rendered uninhabitable when Ceti Alpha Six exploded.
Kirk never bothered to check up on them (and Starfleet astronomy kind of fell down on the job too), and Khan's kind of cranky about it.
He introduces Chekov and Terrell to the local space eels, who crawl inside their ears and turn them into his obedient zombots.
Offscreen, Khan and his gang hijack the Reliant, strand the remaining crew on Ceti Alpha Five, and head off looking for some payback.