The Haywood family train and handle horses for film and television productions. Otis Haywood Sr. is killed by a falling object, which they presume fell out of an airplane. His children Otis "OJ" Haywood Jr. and Emerald "Em" Haywood inherit the ranch. In order to keep the business afloat, OJ sells some of the horses to Ricky "Jupe" Park, who operates a nearby Western theme park named Jupiter's Claim. At the park Jupe also exploits his past as a child actor on a sitcom where a chimpanzee animal actor attacked several of its human co-stars.

One night, the Haywoods notice their electricity fluctuating and their horses vanishing and violently reacting to an unknown presence. They discover an unidentified flying object (UFO) shaped like a flying saucer that has been taking their horses, and then spitting out the inorganic matter, a piece of which caused their father's death. Motivated by a desire to save the ranch by selling footage of the UFO to Oprah, the siblings decide to document evidence of the UFO's existence, and they recruit Fry's Electronics employee Angel Torres to set up surveillance cameras. Electrical interference from the UFO and a mantis on one of the cameras prevent them from getting clear footage, but Angel notices a nearby cloud that never moves. They deduce that it is the UFO's hiding place.

Jupe introduces a live show in Jupiter's Claim and plans to use Lucky, one of OJ’s horses, as bait to lure out the UFO, which he has been feeding the Haywoods' horses to for months, in front of an audience. The UFO arrives but devours Jupe and the entire audience. OJ deduces that the UFO is not a spaceship, but a predatory, territorial creature, and that it eats anything that looks directly at it. Utilizing similar methods to those used to break and train horses, OJ believes that they can influence the creature's behavior, and capture footage of it without being killed. Dubbing the creature "Jean Jacket" after a horse from their childhoods, the Haywoods decide to hire cinematographer Antlers Holst for assistance. Holst initially refuses, but eventually agrees after hearing about the Jupiter's Claim incident.

To circumvent Jean Jacket's effects on electronics, Holst brings a hand-cranked IMAX film camera to capture footage. With Angel, the group devises a plan to bait out Jean Jacket, with a field of electrically-powered tube man props to help them deduce its location in the sky. However, a paparazzo trespasses onto the field and is thrown from his electric motorcycle when it shuts down near Jean Jacket. He is devoured by Jean Jacket while begging OJ to film the event. Though Holst is able to capture footage of Jean Jacket, his obsession with "the impossible shot" results in him being devoured along with his camera. Angel survives an attack from Jean Jacket by being wrapped in a tarp and barbed wire, causing the creature to unfurl from its saucer shape to a jellyfish-like form.

OJ intentionally looks directly at Jean Jacket, allowing Em to use the motorcycle to rush to Jupiter's Claim. There, she untethers the park's large helium balloon mascot of Jupe. Jean Jacket attempts to feed on the balloon while Em uses an attraction's analog camera to photograph Jean Jacket before the balloon pops. With the picture as proof of the creature's existence and reporters arriving nearby, Em sees an unharmed OJ and Lucky standing outside of Jupiter's Claim.