In the aftermath of a choriocytosis outbreak, the crew is doing fine as the disease is no more harmful than pneumonia. However, en route to Deneb V for a dedication ceremony, Spock collapses on the bridge. In Sickbay McCoy informs Kirk that choriocytosis is inevitably fatal to races with copper-based blood. The only known cure is strobolin, a rare naturally occurring drug. The nearest planet with the drug is Beta Canopis, which is four days away at maximum warp. McCoy warns that he can sustain Spock temporarily with a synthetic, but at best he will only survive three days.
Kirk makes arrangements for a rendezvous: the Potemkin will pick up the drug at Beta Canopis, then pass it on to the S.S. Huron for final delivery to the Enterprise. As they proceed to the rendezvous, Kirk and McCoy are forced to order Spock to half duties. However, his condition steadily worsens as the disease suffocates his blood cells, preventing them from absorbing oxygen. The synthetic strobolin soon fails to have any effect and Spock collapses shortly thereafter.
The Huron, a dilithium freighter, picks up the strobolin and proceeds to the rendezvous. However, an unidentified alien ship starts shadowing them. It finally moves to intercept, ignoring all hails that the Huron's captain, O'Shea, sends out. Evasive maneuvers proof useless. As O'Shea sends a distress signal to the Enterprise, the aliens order him to surrender or be destroyed.
The Enterprise receives the distress signal and investigates, and discovers the Huron dead in space. Kirk takes a landing party over and they discover that the crew is barely alive, but the dilithium and the strobolin have been stolen. With only 20 hours left, the ship follows the unique radioactive waste trail left by the alien ship. The trail leads to an asteroid belt consisting of both matter and anti-matter planetoids in close proximity.
The Enterprise enters the asteroid belt and the alien ship opens fire. Its phasers are too weak to penetrate the shields. Arex identifies the vessel as of Orion registry. Unable to flee or destroy the Enterprise, the Orion Captain makes contact and demands that they let him go on his way. He tries to claim neutrality but Kirk notes that Orion's neutrality has been in dispute since the Babel conference and Babel resolutions require the Orions submit to a search. The Orion captain refuses but Arex detects the dilithium aboard his ship. Kirk offers a deal: in return for the strobolin, he'll let the Orions keep the dilithium, receive an additional payment, and no record of the incident. The Orion Captain ponders the matter and suggests a face-to-face-exchange on a nearby planetoid.
With only an hour left for Spock, Kirk agrees to the proposal. Scotty and McCoy warn against it but Kirk has no choice. He does agree to keep his communicator active, and have Scotty monitor him at all times for immediate transport. Aboard the Orion vessel, the Orion Captain realizes that his people's neutrality can't be risked on Kirk's word. His lieutenant comes up with a plan: a nearby asteroid is highly explosive. They can set off a chain reaction with a small dilithium explosion. The Orion Captain agrees and insists on delivering it himself so he can see the look on Kirk's face just before he pulls the trigger.
On the asteroid, the two captains meet. The Orion Captain has the strobolin but informs Kirk that he can't risk Orion neutrality. He starts to trigger the detonation device as Kirk tries to stop him. Aboard the Enterprise, Arex detects the dilithium and informs Scotty, who quickly beams up the dilithium in the trigger device. The Orion Captain activates the device just too late and nothing happens. Kirk grabs him and orders transport. On board the Enterprise, the Orion Captain tries to kill himself but security guards quickly stop him. Realizing that the Orion crew will destroy themselves and their ship, Kirk informs the Orion Captain that their sacrifice will be in vain because they plan to make sure the Orion Captain survives to stand trial. The Orion Captain agrees to order his crew to stand down rather than let them needlessly sacrifice their lives.
Later, the Enterprise proceeds with the Orion ship in tow. McCoy administers the strobolin to Spock, who recovers. McCoy insists on pointing out that this one time Spock's superior physiology endangered his life, but Spock admits he still prefers a Vulcan body to a human, all things considered.