Stardate 3842.3: Kirk and McCoy are preparing their dress uniforms as they arrive at Vulcan to pick up the last delegates for the Babel conference. The shuttlecraft comes aboard and Kirk greets the Vulcan ambassador, Sarek. He introduces him to McCoy and Spock, and Sarek in turn introduces his human wife, Amanda. Kirk offers Spock as a tour guide and Sarek asks for someone else. He then offers Spock a chance to visit his parents… and the science officer notes that Sarek and Amanda are his parents.
Kirk escorts Sarek and Amanda about the ship and into Engineering. Amanda talks privately to Spock and he notes the situation with his father hasn't changed. When Kirk asks Spock to talk about the computers, Sarek notes that his son left for Starfleet against his wishes and Spock leaves. After Sarek leaves, Amanda explains the Vulcan way and how it has kept Sarek and Spock from speaking as father and son for 18 years. They're interrupted by Uhura who reports they've picked up an unauthorized signal.
Kirk notes that the delegates are in disagreement over the Coridan affair that they are traveling to Babel to resolve. Sarek ends up in an argument with the Tellarite ambassador, Gav, while the Andorian ambassador Shras looks on. Kirk interrupts and Gav storms off.
The crew picks up a nearby scout ship at the edge of sensor range but they're unable to identify it. When they approach the ship moves away at Warp 10, well in excess of the Enterprise's speed. Back at the reception, Sarek secretly takes medication and Gav then confronts him again. Sarek admits they'll be voting in favor and Gav lashes out at him. Sarek easily deflects him and Gav storms off. Later a security guard finds Gav dead in a Jeffries tube.
McCoy confirms that Gav's neck was snapped with surgical precision. Kirk notes that Gav was arguing with Sarek and Spock confirms his father has the necessary knowledge, and that if there was a logical reason for him to do so, he could kill quite efficiently.
Kirk, Spock, and McCoy go to Sarek's quarters to find Sarek gone, meditating according to Amanda. Sarek returns and admits he has no alibi, then collapses in pain. McCoy says it's some kind of heart problem but isn't familiar enough with Vulcan physiology to provide an immediate diagnosis.
Later on the bridge, Kirk expresses his condolences but Spock says he isn't worried. Uhura picks up another transmission and confirms it's coming from the Enterprise. Spock is unable to decipher the coded signal.
Kirk meets with McCoy who says Sarek has a heart defect and Sarek admits he's had three attacks which he didn't tell Amanda about. McCoy notes that he can't do the operation because he doesn't have enough blood and Sarek's is rare. Spock's blood is compatible but he couldn't give enough blood to support the operation. Later McCoy and Spock come up with a Rigellian drug that increases blood production but McCoy is reluctant to proceed given his lack of experience with Vulcans. Sarek won't be able to take the stress so Spock volunteers to be a donor. McCoy refuses to sanction it and Amanda agrees, but Spock notes they now have the means to perform the operation.
In a corridor, an Andorian comes at Kirk with a knife. After a struggle, the assassin plants a knife in Kirk's side before taking him down. Kirk manages to call the bridge before collapsing.
They get Kirk to Sickbay while Sarek's condition worsens. However, now that Spock is in command he refuses to volunteer as he is now in command during a crisis situation. Ambassador Shras confirms he doesn't know much about the assassin, Thelev, who has been conditioned against interrogation.
Amanda comes to see Spock and ask him to act as a donor. Spock refuses to dismiss his duties and Amanda tries to appeal to whatever part of him is human. When Spock refuses, she slaps him and leaves.
McCoy tells Kirk of the situation and the captain refuses to let Spock stay in command while sacrificing Sarek. Kirk decides to convince Spock he can take command, then go back to Sickbay afterward. Once Spock leaves the bridge with McCoy, the opposing ship approaches them and Kirk stays in command. Uhura confirms the signal is coming from the brig. The security guards search Thelev and are forced to turn him, dislodging his antenna and revealing a hidden transmitter. The enemy ship approaches the Enterprise and attacks, able to keep ahead of its phasers, while McCoy proceeds with the operation.
Security brings Thelev to the bridge where Kirk confronts him. The captain shuts down power to lure the enemy ship in, and when it comes in Kirk orders a full attack. They disable the enemy ship but it self-destructs before they can offer surrender. Thelev has already taken a slow poison and dies before they can get him off the bridge.
As Kirk goes to Sickbay, McCoy has completed the operation and both patients have survived. Spock reveals that he has deduced that Thelev and the enemy ship were Orion smugglers intending to start an interplanetary war, and then they'd remain neutral and sell weapons to both sides. The ship was constructed for a suicide mission, allowing it to maintain high speed. Sarek sees no reason to thank Spock for acting logically, much to Amanda's frustration with both of them. Amanda relents and when Kirk weakens McCoy gets him into bed. McCoy insists that Spock stay in bed as well and tells them all to shut up, then gloats at getting the last word.