Leonard Nimoy begins the episode hosting a show about alien encounters. He begins talking about an encounter in a town called Springfield.
At Moe's on Friday night, Homer drinks over ten bottles of "Red Tick Beer", a brand that is brewed with real dogs. He takes a breathalyzer test which declares he is as drunk as Boris Yeltsin, and he decides to walk home. However, Homer takes the wrong path and ends up lost and disoriented in the woods. In a clearing, he sees a glowing thin-boned alien. Homer panics and runs away screaming.
No one in the Simpson family believes Homer's story, and his attempts to report the alien to the local police are dismissed. Agents Fox Mulder and Dana Scully of the FBI go to the Simpson residence to investigate. After no results from their psychological tests, which are closely watched by the Cigarette Smoking Man, Homer fails to provide any proof he actually did see an alien. Homer is ridiculed by most of the neighborhood, especially Lisa, but Bart says that he believes Homer. He tells Homer that the reason why he believes him is that he so 'damn' sure, much to Homer's relief. The next Friday night, they camp out in the clearing (with Ned Flanders' camping equipment) and they both see the alien, Bart for the first time. The alien promises peace before Homer scares him away by screaming as he accidentally steps in their campfire. Homer is upset about missing the chance to obtain proof, until Bart tells him that he captured the entire incident on tape (with Flanders' video camera). Homer and Bart cheer as they now have evidence of the alien.
Leonard Nimoy closes his narration, ending the story with Homer and Bart having obtained proof of their alien encounter. He then says goodnight to the viewers, but the Squeaky-Voiced Teen (offscreen) reminds him that the show still has ten minutes left. Nimoy leaves anyway, running to his car and driving away. The Squeaky-Voiced Teen takes over the narrating duties.
Although Bart's tape is only three seconds long and is mostly static, only briefly showing the alien, everyone in Springfield starts to believe Homer (Lisa still isn't convinced). Friday comes again and all Springfielders go to the clearing (among them Leonard Nimoy). Sure enough, the alien appears, promising love. Dr. Hilbert asks if the alien means love between a man and woman, or love between a man and his cigar. The Springfielders begin to riot until Lisa shows that the "alien" is actually Mr. Burns. Smithers states that Burns receives longevity treatments once a week to cheat death for the next seven days, and the process leaves him twisted and disoriented, and with a sweet heavenly voice (due respectively to a chiropractic treatment, anaesthesia, and a throat-scraping).
Back to his normal self, Burns reveals that his green glow is due to many years of working in a nuclear plant, and then renounces his promises of peace and love and instead says that he brings famine and hatred. Before he can say anything else negative, Burns receives a booster shot from Dr. Nick and everyone sings "Good Morning Starshine" along with him. Marge apologizes to Homer for not believing him and the two reconciled. The Squeaky-Voiced Teen ends Nimoy's show, telling the viewers to "keep watching the skies," although he mispronounces "skies" in doing so.