Penny is a very harried housewife with a dim-witted and hapless husband, Russell, and four children: Janet and Susan, who are always fighting; Gertie, who is very clumsy; and Russell Jr., who is always playing pranks. A typical morning consists of Penny being awakened by her excessively loud clock radio, cooking breakfast while Janet and Susan fight and interrupt her, Russell Jr. playing a prank, Gertie spilling something, Russell complaining about something, the phone ringing, the dog barking, and the washing machine acting up.
One day, Penny works in her garden while her neighbor loudly removes tree limbs with a chainsaw. As she digs, she discovers a wooden box containing a beautiful gold pendant in the shape of a sundial. Not thinking anything of it, she takes it inside and puts it on.
At the grocery store, Penny is harassed by the whining Gertie and Russell Jr. and by annoying customers. While driving home as Janet and Susan loudly fight, she seems to be on the verge of a total nervous breakdown. While she tries to cook dinner, her children begin to pester her again and her husband comes downstairs complaining about a rip in his shirt. As the noise level becomes too much, she yells at them to shut up—and they freeze in time. She is confused at first, but soon realizes that the pendant is an amulet that can stop time. She tells her family to start talking and time restarts. She is happy as she realizes that she will finally have a little peace and quiet. "Shut up" is the phrase to stop time and "start talking" restarts time. However, the power will only work if Penny is wearing the amulet.
Later that night, Penny watches a news program about the recent peace talks between the United States and the Soviet Union. She becomes annoyed and briefly freezes time, then expresses her happiness and goes to sleep.
The next day, Penny uses her time-stopping power to enjoy a peaceful breakfast with her family, to shop at the grocery store without incident, and to avoid being pestered by two anti-nuclear weapons activists; she drags their frozen bodies into the yard, lays them down, then restarts time, and the shocked activists decide to skip her house.
Later that evening, Penny enjoys a relaxing bath when air raid sirens go off and she hears her husband calling loudly from the bedroom. When she goes into the bedroom, the radio announcer reveals that nuclear missiles are heading for the United States. When the radio reveals that ICBMs have entered U.S. airspace and Russell and Russell Jr. begin to weep, Penny, overwhelmed, screams at everyone to SHUT UP...and quickly freezes time just as an explosion is heard in the distance. She then leaves her house and walks through the frozen town. She looks up to see what the frozen, terrified people are looking at... and is horrified to see a Soviet nuclear missile frozen a few hundred feet above a nearby theater, nose down and presumably moments from detonating.
The episode ends with Penny facing an impossible dilemma: Will she live eternally alone in a silent, but safe, world... or unfreeze time to be destroyed by nuclear war?
This episode is similar in theme to two episodes of the original series; "Time Enough at Last" which involves a man who seeks a refuge from life while reading when the world ends through a nuclear war, and "A Kind of a Stopwatch" which involves a man who gains the power to stop time using a stopwatch.
The ending is also similar to a short story by Arthur C. Clarke entitled "All the Time in the World", which concludes with the lead character in possession of a time-stopping device moments before a nuclear super bomb test ends the world. That story was adapted for television by Tales of Tomorrow, a forerunner to the original Twilight Zone series.In the final scene, the two films playing in the theater when Penny stops time are Dr. Strangelove and Fail Safe, two 1964 films which both depict nuclear warfare.