Assistant Federation Commissioner Nancy Hedford has become ill while trying to stop a war on Epsilon Canaris III. The shuttlecraft Galileo is assigned to take her to the U.S.S. Enterprise, where she will receive treatment for the otherwise fatal Sakuro's disease. En route, the shuttlecraft is pulled off course by a mysterious, cloud-like entity. Deposited safely on the planet Gamma Canaris N, Kirk and his party meet Zefram Cochrane, the scientist that invented warp drive on Earth over 100 years before.

Glenn Corbett (Zefram Cochrane)
Elinor Donahue (Commissioner Nancy Hedford)
James Doohan (Lt. Cmdr. Montgomery Scott)
George Takei (Lt. Hikaru Sulu)
Nichelle Nichols (Lt. Uhura)

• The shuttle Galileo was destroyed in the episode "The Galileo Seven".
  
• Zefram Cochran's first warp flight will be shown in the motion picture Star Trek: First Contact.