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Her crew still recovering from a recent shipwide outbreak of choriocytosis, the Enterprise is en route to the dedication ceremonies for Deneb V's new Academy of Sciences. On the way, Commander Spock succumbs to the very disease from which the rest of the crew has already recovered. Because Vulcans have copper-based blood, choriocytosis — which afflicts humans no more severely than does pneumonia — will prove fatal to Spock, unless a supply of a counteragent known as strobolin can be found within three days' time.

The closest source of the drug is the planet Beta Canopis, which is four days away at maximum warp. However, Kirk arranges to have the U.S.S. Potemkin pick up some strobolin and hand it off to the freighter S.S. Huron, which is headed in the Enterprise's direction. Unfortunately, an unknown vessel attacks the Huron before the rendezvous can take place, and relieves the freighter of her cargo of dilithium and strobolin. The Huron's Captain O'Shea doesn't know the identity of the attackers, but Kirk immediately sets out to discover it, while Spock grows ever weaker from the effects of his advancing choriocytosis.

Following the marauding ship's unique radiation trail, the Enterprise soon catches up with the culprit: an Orion vessel. After some bargaining with the Orions, Kirk and the Orion captain agree to meet on a nearby asteroid, where the pirate leader has consented to hand over the strobolin. Though Kirk is aware that he's walking into a trap, Spock's deteriorating condition leaves him little choice. The Orions secretly plan to double-cross Kirk by detonating a dilithium bomb on the geologically unstable asteroid, but Chief Engineer Scott beams the dilithium out of the device in the nick of time, and beams Kirk and the Orions aboard the Enterprise as well. Captured and prevented from taking his "suicide pill? — Orion operatives are supposed to kill themselves rather than be captured — the Orion captain and his crew now must face trial for the crime of piracy. Spock recovers from choriocytosis, thanks to the recovered strobolin, although he must endure Dr. McCoy's good-natured jibes about his green Vulcan blood turning out to be a liability for once.