The Enterprise visits Ligon II to obtain a rare vaccine needed to avert a plague on Stryis IV. As the Ligonian leader, Lutan, comes on board, he seems very arrogant, and more than slightly attracted to Tasha, but not dangerous. Unfortunately, in departing, he kidnaps Tasha from right under the Enterprise's noses.

Data and Riker theorize that Lutan kidnapped Tasha as a display of "counting coup"-by stealing the riskiest prize of all, he proved himself very brave for his followers. By Ligonian custom, Picard must ask to get Tasha back, in public, at a banquet. He does this, but Lutan says that he cannot part with her, thus breaking even his own customs. His wife, Yareena, challenges Tasha to a death-duel, which she must accept if the Enterprise is to obtain the vaccine (and it's needed quickly, as the plague is growing ever worse...). Lutan now cannot lose; if Yareena dies, he inherits all her land (on Ligon, the women own the land), and if she lives, he loses nothing.

The crew tries to talk everyone out of this, to no avail. Then, they turn from diplomacy to deception. Yar wins the duel, killing Yareena with the instantly-lethal poison used on the weapons. They then both immediately beam up, where Beverly saves Yareena. Having come back from the dead, Yareena's marriage to Lutan is dissolved. She chooses his second, Hagon, as husband, and the ship leaves, with both Tasha and the vaccine.