Captain Kirk and Dr. McCoy travel to a hospital facility on Vulcan to acquire treatment for a badly wounded Enterprise crew member. Kirk encounters Spock's mother, Amanda Grayson, and Spock's father, Sarek, and soon becomes heavily involved in Spock's personal life.
Then people begin to die. Kirk, trying to solve the case, is hampered by some Vulcans' belief that it would be illogical for murder to be happening on their home world, and that the deaths are therefore accidents. But he knows criminal behavior when he sees it, and presses on.