Act I

Visit to a Small Planet begins with a glimpse into the home of Roger Spelding, a television news commentator, situated in a comfortable middle-class neighborhood near Manassas, Virginia. General Tom Powers, a friend of Roger's, informs him that an Unidentified Flying Object (UFO) has been seen hovering above the Spelding residence for the past twelve hours. Despite Roger's skepticism, Powers persuades him to take a look outside, where Roger indeed sees the UFO. Originally intending to tell his television audience that UFOs are nonexistent, Roger becomes frantic and asks Powers for permission to report the sighting. The general denies his request, stating the information is "classified."

Roger's nineteen-year-old daughter, Ellen, appears on the terrace with her boyfriend, Conrad Mayberry, whom Roger dismissively calls "the boy farmer." As they discuss their future plans, they are interrupted by the UFO landing outside the house. The hatch opens, and Kreton, an extraterrestrial visitor, enters the room. Kreton, who resembles a human from the 1860s with side-whiskers and period attire, requests to be taken to General Robert E. Lee. After some initial confusion, Kreton explains that Earth has been his 'hobby'; he intended to witness the Civil War Battle of Bull Run. However, he realizes he miscalculated the coordinates for his time-traveling spacecraft. Roger, hoping to interview Kreton on his television show, invites him inside, and Kreton eagerly accepts, excited to see "a real house."

General Powers returns with an aide and begins questioning Kreton in Roger's study. It is revealed that Kreton not only hails from another planet but also from another dimension, where beings do not die and can read minds—a skill Kreton demonstrates to the general. Ordered by Powers to inspect Kreton's ship, the aide reports back that the door is sealed, and "some kind of invisible wall" has been erected around it. When Powers inquires about the creation of this force field, Kreton wryly replies, "I don't think I could ever explain it to you." Powers then declares that no one is permitted to leave the house. Continuing his investigation, the general speculates that Kreton "has been sent here by another civilization for the express purpose of reconnoitering prior to invasion." Kreton refutes the idea that he was "sent here" by anyone, but admits he plans to "take charge" of the entire world. When Powers attempts to arrest him, Kreton envelops himself in another invisible force field. As the curtain falls, the audience hears the characters' thoughts and Kreton's voice saying, "Tomorrow will be a wonderful day for all of us. Sleep tight!"

Act II, Scene 1

The following morning, Kreton is in the living room studying a globe and conversing with Rosemary, the Speldings' cat. He can read and understand her thoughts. Roger has gone to Washington with General Powers, Reba (Roger's wife) has been given permission to go shopping, and Conrad is still asleep upstairs. Ellen brings Kreton breakfast, which he declines because he doesn’t eat. He tells Ellen that the people of his world have stopped reproducing since they are immortal. He further explains that after eradicating diseases like scarlet fever, mumps, and the common cold, they eliminated "the ultimate disease:" passion. Kreton states, "We feel nothing. We do nothing. We are perfect." Ellen discovers that this absence of passion or strong emotions was what drove Kreton to visit Earth and escape his dull commander, Delton 4.

Ellen and Kreton become more acquainted, and Ellen persuades the alien to teach her the mind tricks he has been using throughout the play. Eventually, she manages to levitate a vase over the fireplace mantle for a few...