The Enterprise is given the mission of transporting the Medusan ambassador Kollos, a member of a species so ugly that the mere sight of it causes humans to go insane, back to his home planet. Spock is able to wear a visor which will protect him, but all humans are forced to leave the bridge before the ambassador arrives. The ambassador arrives enclosed in a specially designed box, but is also accompanied by the telepath Dr. Miranda Jones, who is looking after his needs. Like Spock, Jones is able to look at a Medusan through a visor, supposedly because she has studied on Vulcan.
Larry Marvick, one of the designers of the Enterprise, also has beamed aboard. He is in love love with Jones. At a welcoming dinner, the senior crew all drool over Miranda, but the mood is spoiled when she reports that someone nearby is contemplating murder. When Marvick's advances are snubbed by Miranda, she discovers that he is the one considering murder, although she does not know whom against. Marvick seeks revenge against Kollos for taking Miranda away from him, but is driven insane when he inadvertently looks at Kollos while attempting to shoot him with a phaser. The insane Marvick commandeers the Enterprise, pilots it to an unknown location outside of the galaxy, raves about being suffocated in his sleep, and then dies for no apparent reason.
In order to return the Enterprise to the galaxy, either Spock or Miranda must mind meld with the ambassador who, as all Medusans, is a master navigator. Spock is given the task, but fears interference from Miranda, who is fiercely jealous of Spock's ability to mind meld. Kirk discovers that Miranda is afraid of human emotion, and wishes to go with Kollos partly to avoid having to deal with it. However, she learns of Spock's plans telepathicaly, and demands that she be taught to pilot the Enterprise so that she can mind meld with Kollos. Bones uses the opportunity to reveal that Miranda is blind (her dress is a highly complicated sensor web which allows her to see, as well as to measure Kirk's distance from the door as 1 m 4 cm), which is why she is able to ``look'' at Kollos.
Kirk suggests that Miranda take up the issue with Kollos, who agrees to her horror that Spock should be the one to make contact. Using the visor to protect his Vulcan half from the sight of the Medusan, Spock melds minds. A now smiling and cheerful Spock greets the other senior crew members, then pilots the ship successfully back to the Milky Way. However, when Spock reverses the mind meld, he forgets the visor, sees Kollos, and goes crazy.
Kirk asks Miranda to help Spock, and when she claims to do be able to do nothing, Kirk accuses her of having used her mental powers to make Spock forget to put on the visor. Luckily, Miranda has a change of heart and uses telepathy to bring Spock back to health.
Miranda and Kollos are then delivered to their destination. Upon parting, Kirk presents Miranda with a rose. Miranda queries ``I suppose it has thorns,'' and Kirk responds, ``I never met a rose that didn't.''