The Enterprise has used the light speed breakaway factor to propel itself backward in time. It monitors Earth communications while on a historical fact-finding mission to study how Earth survived the turbulent year 1968.
While in orbit, the Enterprise accidentally intercepts a transporter beam originating more that 1000 light years away, beaming aboard interplanetary agent Gary Seven and his partner Isis, disguised as a black cat. Seven discovers that the Enterprise is from the future, and demands to be beamed down to continue with his mission. Seven claims he is a human from the twentieth century who has been living on a different planet, which wishes to remain hidden (even is Kirk's time). When Kirk decides to confine Seven to a detention cell until he can learn more, Seven overpowers the guards and even brushes off Spock's nerve pinch, but Kirk temporarily stuns him with a phaser. Ho does not long remain in his cell, however, using a ``servo'' device disguised as a pen to deactivate the force field and put his guard to sleep. He is rejoined by Isis on his way to the transporter room, and beams down before Kirk can stop him, materializing inside a safe concealed behind a sliding rack of glasses in what appears to be an otherwise normal office.
However, the office turns out to be anything but normal, and a Beta 5 computer (capable of analytical decision) is also hidden behind a bookcase. Gary Seven asks the Beta 5 computer the status of agents 201 and 347, and discovers that their location has not been reported for 3 days. In order to access the computer, Gary Seven (who is known as agent 194 and turns out to be a ``Class 1 Supervisor''), is forced to summarize the nature of his mission. The agents turn out to be descendants of human ancestors taken from the Earth 6000 year ago and specially trained for the mission of preventing Earth from destroying itself before it can become a peaceful society. According to the computer, this is necessary since science and technology have progressed faster than political and social knowledge on Earth. Seven learns that the agents' mission was to disable a rocket to launch an American orbiting nuclear platform which will take off in an hour to counter a similar platform launched by an ``opposing power.'' Seven compares this situation to the one which almost resulted in the destruction of planet Omicron 4.
Meanwhile, Roberta Lincoln, a secretary hired by Seven's fellow agent shows up (late) for work, and Seven mistakes her for one of the agents. As a result, he shares some of his secret gadgetry with her, including a voice-activated typewriter. However, Seven convinces her that he is a CIA agent, and that she should remain silent about what she has seen in the interests of national security.
Just after Seven learns from the Beta 5 that agents 201 and 347 were killed in an automobile accident on Highway 949, 10 miles north of McKinley Rocket Base, Kirk and Spock (who have beamed down in an attempt to locate Seven) barge into the office. However, Lincoln stalls them long enough to allow Seven to escape into the safe/transporter, and also manages to call the police to the office (which is located at 811 East 68th Street, number 12B). When they arrive, Kirk beams them up to the Enterprise along with himself and Spock, then immediately returns the policemen to the apartment.
Seven rematerializes inside the rocket base and stuns a guard with his pen gizmo before he can complete a call to security. Seven then makes his way to the gantry elevator and begins to sabotage the wiring when he reaches the top. Just as the guard stunned by Seven awakes, Kirk and Spock materialize in front of him and are escorted by him to an interrogation in the launch complex.
Meanwhile, Lincoln accidentally discovers the sliding glass rack, opening it by depressing a pen on the desk. She then picks the lock to the safe. At the sane time, Scott locates Seven manipulating wires on the rocket using the ships sensors, and attempts to beam him up. Lincoln, however, accidentally pulls him back to the office while fiddling with the safe controls. Seven then using the Beta 5 exceiver circuits to cause the third stage of the American rocket to malfunction and veer off course. He also arms the warhead, and is shortly thereafter konked on the head by Roberta.
The arming of the warhead is noted by Chekov aboard the Enterprise, who attempts to contact Kirk for instructions. When the communicator beeps and the rocket base guard picks it up, Spock nerve pinches the guard, and tells Scott to beam Kirk and himself to Seven's apartment. Here, they watch while Seven explodes the warhead 104 miles above ground. Records from the Enterprise show that exactly such an event occurred, and that it furthermore caused the nuclear powers to re-assess the risks of placing hydrogen bombs in orbit.