The Enterprise transports ambassadors to a conference to discuss the admission of Corridon, a star system composed of many mutually combative races, to the Federation. Corridon contains a nearly unlimited supply of dilithium crystals, but its small population and lack of strong government has allowed illegal mining operations by outsiders seeking to exploit its natural resources. Sarek is the 102.437-year-old ambassador from Vulcan, and is accompanied by his wife Amanda (who is a human). To Kirk's surprise, they turn out to Spock's parents. Also to Kirk's surprise, Sarek is cool towards Spock, apparently because Spock has chosen to devote his life to Starfleet instead of Vulcan science.
The conference is to take place on neutral planet code-named Babel. McCoy questions Amanda about Spock and finds that, as a youth, he had a pet sela, a sort of fat Vulcan Teddy bear with 6-inch fangs. Meanwhile, Uhura has detected an unidentified transmission from the Enterprise, and Chekov subsequently detects a small ship of unknown origin paralleling the Enterprise just out of phaser range at Warp 10.
From Section A3 on Deck 11, Lt. Joseph reports that Tellerite ambassador Gav has been murdered. McCoy ascertains that death was instantaneous following an expert breaking of his neck (known to Vulcans of Tel-Shaha). This brings Sarek under suspicion, since he had been involved in an altercation with the Tellerite after accusing his people of smuggling from Corridon. However, when Kirk begins asking Sarek questions, Sarek suffers from a malfunction in one of his heart valves, the Vulcan equivalent of a heart attack.
Meanwhile, Spock detects tritanium emissions from the alien ship's hull after it transmits a message. Uhura determines that the message was received somewhere aboard the Enterprise. However, Spock is unable to decode the fragment of the message which Uhura has intercepted.
Sarek reveals that he has had three previous Vulcan heart attacks, and has been taking Bengacydrine to combat it. He requires an open heart operation, but the ship's stores do not have a sufficient supply of blood, especially of Sarek's rare Vulcan T negative blood. Despite the fact that Spock's blood is a mixture of human and Vulcan factors, he provides a blood transfusion to Sarek after McCoy uses an experimental stimulant to increase the rate of blood production.
The Andorian Thelev, a minor member of the ambassador's staff, attacks Kirk near Deck 5 and stabs him. Kirk requires medical attention, so Spock assumes command. Under these circumstances, he says he cannot take time off to give the transfusion to Sarek, and cannot pass command on to anyone else because he is the best qualified person to command the Enterprise. His mother pleads with him, but he refuses.
Finally, Kirk pretends to be healed (with McCoy's reluctant approval) and takes command from Spock, ordering him to sickbay. Uhura detects another transmission originating from the Enterprise,, and this time it is pinpointed to the Andorian in the brig. A search by security reveals a transceiver hidden in one of his fake antennae.
The Enterprise is then attacked by alien ship while Sarek and Spock are on the operating table, endangering both their lives. It is moving too quickly to be hit by the Enterprise and is able to damage the Enterprise sufficiently that it loses one of its shields. Kirk fools the alien ship by turning off shields and internal power, luring the enemy ship in for the kill. When it begins moving in, Kirk hits it with phasers and disables it. However, before he can ask them to surrender, they blow themselves up.
The Andorian prisoner appears to have been attempting to sow discord and distrust among the Federation members, but he dies of self-administered slow poison shortly after his comrades' ship is destroyed by the Enterprise. However, Spock, who is recovering from the operation, surmises that the perpetrators were from Orion, since Orioners are known to have been smuggling dilithium from Corridon and are anxious to prevent interference. McCoy confines both the injured Kirk and the recovering Spock to sickbay, shushing all protests. ``Well, what do you know,'' he says with a grin, ``I finally got the last word.''