The Enterprise is at Vulcan, on a mission involving carrying ambassadors of Federation planets to a conference on the neutral planetoid code-named Babel. Kirk, Spock and McCoy greet Ambassador Sarek, and his wife Amanda, welcoming them aboard. They are courteous to the crew but pointedly avoid Spock. Later, Kirk asks Spock if he would like to take advantage of the stopover to visit his parents on Vulcan. To his amazement, Spock calmly replies that Sarek and Amanda are his parents.

During a tour of the ship, Kirk queries this with Amanda after Sarek has left them for his quarters. She tells him that Spock and Sarek have not spoken for eighteen years after Spock went against his wishes and joined Starfleet. Kirk receives a message from Uhura telling him that she is getting a strong signal on her panel from somewhere aboard ship but cannot pinpoint the location or decode it.

Now under way to Babel, a reception is held for the conference delegates during which Gav, the Tellarite ambassador, insists that Sarek tells him how he is going to vote on the Coridian application to join the Federation but is interrupted by Kirk's diplomacy. Sarek and Amanda retire to their quarters while Kirk receives a summons to the bridge by Chekov. His sensors have detected a small, unidentified craft that seems to be shadowing them. On turning to intercept it, the mysterious ship makes off at high speed. Sarek returns to the reception and is again accosted by Gav. This time, Sarek tells him that Vulcan will vote in favour of Coridian, at which point the Tellarite tries to attack him.

The Vulcan's superior strength brushes him aside easily and Kirk arrives to prevent a more serious incident. Later that evening, Gav's body is found with a broken neck, hanging in a Jefferies tube, by Lieutenant Joseph. Spock comments that the technique used is consistent with Tal-Shaya, a form of execution used on Vulcan, and that Sarek could have committed the murder if he had a logical reason to do so. On being asked where he was at the time of the murder, Sarek tells them that he was on his own in private meditation, then collapses in front of them. McCoy's examination proves inconclusive but he suspects a heart problem of some sort.

On the bridge, Uhura picks up the strange transmissions again. Kirk and Spock visit sickbay where McCoy confirms his first suspicions on Sarek's condition. He needs to perform an operation on Sarek immediately in order to save his life but only Spock has the same rare blood group. Spock cannot supply enough blood for the surgery by himself and persuades McCoy to use a dangerous experimental drug to increase his body's blood production rate. Sarek admits to them that he has had previous attacks and was actually suffering from one at the time that Gav was murdered.

After leaving sickbay, Kirk discovers an Andorian behaving suspiciously and gets involved in a fight. Despite being stabbed, Kirk manages to overpower the blue-skinned alien and activate an intercom before collapsing. McCoy advises Spock that Kirk will be all right but has been badly injured. He also informs him that the surgery on his father must go ahead immediately or Sarek will die, and is shocked when Spock refuses to help until the Enterprise is safe. When he awakes, Kirk is told about the situation by McCoy and, despite the doctor's protests, gets dressed and persuades McCoy to help him to the bridge.

Spock is surprised to see an apparently healthy Kirk arrive but hands over command and leaves the bridge, accompanying McCoy to sickbay. After the turbolift doors have closed, Kirk slumps weakly into the captain's seat. The mysterious vessel comes closer and signals are intercepted emanating from the brig. Security is despatched to search the Andorian, who resists, and during the struggle one of his antennae breaks off revealing a hidden transmitter. The ship attacks the Enterprise causing it to rock violently and seriously interfering with McCoy's operation on Sarek.

Kirk orders a power shutdown aboard ship to try and fool the enemy into thinking that they are disabled. As the smaller craft closes in, Chekov hits it with phaser fire, following which it self-destructs. On seeing this, the 'Andorian' takes a poison tablet and dies. The immediate crisis being over, Kirk struggles back to sickbay where he finds two unharmed Vulcan patients sitting up in bed. Spock tells Kirk that he believes the attackers and the fake 'Andorian' were Orion smugglers who have recently been raiding Coridian in order to disrupt the conference and provoke war. McCoy orders Kirk to bed and tells both him and Spock to be quiet, finally getting the last word for once.