Leonard Nimoy begins the episode hosting a show about alien encounters. He talks about an encounter in a town called Springfield.
At Moe's on a Friday night, Homer drinks ten beers, and after insisting he takes a breathalyzer test where Homer reaches "Boris Yeltsin" level, Moe declares that he is drunk and will not let him drive. Homer decides to walk home, but takes a wrong path and ends up in the woods. In a clearing, he sees a glowing thin-boned alien. Although the alien says "Don't be afraid", Homer panics and runs home screaming.
The rest of the family do not believe Homer's story, believing it to be a drunken hallucination, and his attempts to report the alien sighting to the local police are dismissed. Agents Fox Mulder and Dana Scully of the FBI hear of the sighting and go to investigate. After receiving no results from their psychological tests of him (which involved Homer making a polygraph explode and jogging on a treadmill (which served no purpose other than Scully wanting Homer to lose some weight), Homer fails to provide any proof that he actually did see an alien, including bringing the agents to the clearing where he saw the alien, which only succeeds in coming across a lost and confused Grampa. Homer is ridiculed by most of the neighborhood; even Marge refuses to believe in his claims and demands he forget about it, but Bart admits that he does believe what Homer is saying. The next Friday night, the pair camp out in the forest. The alien arrives and promises peace, but Homer scares it away when he accidentally steps on their camp fire and screams in pain. Fortunately, Bart captured the entire incident on tape, and Homer thanks him, cheering for the evidence of the alien in their hands.
Leonard Nimoy tells the viewers goodnight. He is then reminded that the show still has ten minutes left by an off-screen Squeaky Voiced Teen, at which point he runs to his car and leaves. The Squeaky Voiced Teen takes over the narrating duties.
Following the successful capture of the alien's existence, Homer and Bart present it to the media. Although Bart's tape is only three seconds long and is mostly static, everyone in town finally believes Homer, including Marge, who apologizes to Homer for doubting him. Lisa, on the other hand, refuses to believe this and maintains that there should be a more logical explanation. Friday comes again and everyone, including Leonard Nimoy and Agent Scully, goes to the forest. Sure enough, the alien appears again, promising love. The townspeople begin to riot, and charge at the alien. Lisa and Waylon Smithers stop them just in time, showing that the "alien" is actually Mr. Burns. Smithers explains that Burns receives longevity treatment once a week in order to cheat death for a further seven days; this leaves him twisted and disoriented, as well as giving him a soft, high pitched voice as a result of a vocal cord scraping. Back to his normal self, Burns reveals that his green glow is due to many years of working in his nuclear plant, and then renounces his promises of peace and love and instead says that he now intends to bring fear, famine and pestilence, shortly before receiving another booster injection from Dr. Nick. He instantly reverts to his "alien" self; he begins to sing "Good Morning Starshine", with the entire crowd (including Mulder, Scully, and Chewbacca) joining in as the sun rises over the clearing. Squeaky-voiced Teen closes the episode by telling the viewers to watch the skies (he momentarily mispronounced it as skis).