The U.S.S. Enterprise pursues an unknown ship into an asteroid belt to save its crew before it's destroyed. The four people aboard are beamed on to the U.S.S. Enterprise; former nemesis Harry Mudd and three beautiful, sultry women: Ruth Bonaventure, Eve McHuron and Magda Kovacs. Mudd was transporting the three women to Ophiuchus VI to marry settlers there.
The Enterprise computers reveal that Mudd has been charged with a number of infractions of the law. In pursuit of Mudd's ship, the U.S.S. Enterprise has burned out its lithium crystals, which power the starship's engines, and Kirk orders them to proceed as quickly as possible to the nearest lithium mining planet. That planet is Rigel XII, which is inhabited by only three lithium miners.
Mudd manages to contact Ben Childress, the head miner, and make a deal with him. Mudd promises to deliver the three beautiful women to the lonely miners in exchange for lithium crystals and their help in escaping Kirk.
Upon reaching the planet, Eve tries to escape, having fallen for Kirk and not wanting to marry one of the miners, but Ben Childress brings her back. They discover that the women are using an extremely illegal Venus drug to make them beautiful and without which they become quite plain. By the time the fraud is discovered, Magda and Ruth are already married to the miners, to the satisfaction of all parties involved. Eve, who realizes that Kirk is married to his career and to his starship, settles for marrying Ben. Kirk gets the lithium crystals he needs for the U.S.S. Enterprise and Harry Mudd, on whom he has filed criminal charges.