The Starship Enterprise is sent on a mission to try and exit the galaxy; all previous attempts at this had failed. En route, it discovers a black box left behind by the last ship to make the attempt, the S. S. Valiant, which reveals only that just prior to the destruction of the ship; the crew has been searching for information about extra-sensory-perception.
When it reaches the edge of the Galaxy, Kirk's friend, Lieutenant Gary Mitchell, is changed somewhat. He gradually becomes more mentally powerful and eventually develops telekenesis. A ship's doctor, Elizabeth Dehner also exhibits similar symptoms, and the two become close.
Mitchell becomes increasingly arrogant, declaring his wish to rule over humans. Kirk is forced to exile them to a remote planet; but he escapes. Eventually, Kirk corners them. Dehner turns against Mitchell, and is killed by him; and Kirk, whilst Mitchell was distracted manages to kill Mitchell himself.