The Enterprise is on a top secret mission to the Tellun star system. It takes aboard Petri, ambassador from Troyius (the outer planet), then continues on the the inner planet Elaas. Here it beams aboard three Elaasian guards who check that all is secure, then the haughty Dohlman of Elaas. Kirk is surprised by her bearing (she demands that Kirk and everyone else, whom she calls inferior, ask her permission to enter and leave her presence). Petri explains that Elaan is to be taken to Troyius for a marriage with the ruler of Troyius in order to stop a bloody war. The Elaasian Council of Nobles and Troyius Tribunal have agreed that Petri shall teach Elaan the customs of Troyius (i.e., the rudiments of civilized behavior), but Elaan has other ideas. She also complains and hurls things about the room when she is unsatisfied with her quarters (which are Uhura's personal quarters which she has vacated for Elaan).
At Petri's request, Kirk proceeds on to the return trip on impulse engines only so as to allow plenty of time for Elaan's ``education.'' Not surprisingly, the lessons do not go well, and Elaan stabs Petri in the back with a knife (fortunately not fatally). To make matters worse, the Federation commissioner sends a coded signal to the Enterprise that he plans to attend the wedding personally.
Meanwhile, Spock detects a ``ghost'' paralleling the Enterprise's course. After fading in and out of sensor range, it finally ventures closer and reveals itself to be a Klingon warship. The reason for the presence of the Klingon warship turns out to be that the Elaasian guard Kriton, is in love with Elaan and has thrown in with the Klingons in a fierce jealousy over having to give up Elaan to the Troyian leader. Kriton booby-traps the warp engines, killing an engineer who discovers and tries to question him.
Kirk tries to take over the tutoring, but doesn't get much further than Petri and has a knife thrown at him. Despite Elaan's orders to the contrary, Kirk enters her chamber (after Spock stuns the two guards) and attempts to administer another lesson. At first, Elaan tries again to kill him. She then locks herself in a closet and tells Kirk that she will wait there 10 ``light-years'' if she has to, but then has a change of heart. She cries and tells Kirk she wants to make people like her. Kirk unwisely touches her tears (which contain a biochemical substance which causes men to fall in love with their shedder), and is snared.
Kriton transmits a signal to the Klingon ship using a Klingon communicator, but is then caught. Before Spock can use the Vulcan mind meld on him, he uses a concealed phaser to commit suicide. The Klingon ship then heads for the Enterprise at warp speed. Luckily, just before Kirk gives orders to maneuver, Scott discovers that the matter-antimatter pods are rigged to explode as soon as the Enterprise goes to warp speed. The Klingon ship streaks by the Enterprise without firing, presumably waiting for it to go to light speed and blow itself up. Unfortunately, Scott finds that the dilithium crystals have been completely fused, and that power for the warp drive and phasers is therefor not available. The Klingons demand that the Enterprise prepare to be boarded or destroyed. When Kirk does not comply, the Klingon attacks.
Spock has been wondering why the Klingons are interested in Elaan in the first place, but discovers the reason when Elaan comes to the bridge and bridge sensors show that the ``common stones'' in the Dohlman's necklace are made of dilithium crystals. Scotty is able to effect repairs to the engines using the crystals, and Kirk blows up the Klingon using photon torpedoes on its next pass. Kirk is able to resist the effects of the tears (to McCoy's's annoyance, since he has actually managed to find an antidote), and the Dohlman is transported safely to Troyius.