The film begins at 62 West Wallaby Street on Gromit's birthday. After falling
downstairs from his bed via a trapdoor in the ceiling, Wallace (voiced by
Peter Sallis) is greeted
with a large pile of bills. Meanwhile, Gromit subtly attempts to remind Wallace
that it is his birthday. After surveying their depleted funds, Wallace lets
slip that he has not forgotten Gromit's birthday after all and presents Gromit
with a somewhat unwelcome gift of a dog collar, and a second present of a pair of ex-NASA robotic "Techno Trousers", designed to
alleviate the burden of taking him for walks. While Gromit is out on a "walk",
Wallace decides that the only solution to their financial problems is to let the spare bedroom out. Thus, a lodger, an inscrutable-looking penguin named Feathers McGraw, comes to stay in the house, pushing Gromit out of his comfortable bedroom and winning Wallace's favour. Upset that Feathers has intruded on his relationship with his master, Gromit leaves home in the rain. Viewing his departure, Feathers goes to work on altering the Techno Trousers for his own means.
After sleeping rough, Gromit hunts for suitable lodgings, noticing a police poster depicting Feathers with a rubber glove on his head and the caption: "Have you seen this chicken?". Meanwhile, Wallace's normal morning routine is interrupted by the replacement of his expected trousers with the modified Techno Trousers. Trapped inside the robotic garments, Wallace is sent on an extended test run, driven by remote control, although he is unaware of Feathers' involvement. Meanwhile, Gromit, seeing this spectacle and having observed Feathers suspiciously measuring up the exterior of the town museum, decides to sneak back into his old bedroom, uncovering Feathers' plans to steal a giant diamond from the museum using the trousers and Wallace as tools. However, Gromit is too late to foil his plan and is forced to hide inside Wallace's bed, where he observes Feathers in his chicken disguise. Wallace, in a deep sleep after the day's misadventures, is unwittingly brought into the robbery by Feathers, and by nightfall breaks into the museum. Feathers uses the suction feet on the trousers to scale the wall, enter the building through an air vent and walk along the ceiling, avoiding the laseralarm system. The helmet Wallace is dressed in contains remote-controlled grabs that hook the diamond. The diamond has barely been hooked when a loose ceiling tile puts the trousers off balance, causing the hook to set off the alarm. This wakes Wallace, who has no idea where he is. After marching Wallace out and back to West Wallaby Street, Feathers reveals his identity and locks Wallace in a wardrobe.
As Feathers makes for the door with the diamond, Gromit confronts Feathers with a rolling pin. Feathers pulls out a revolver and puts Gromit into the wardrobe along with Wallace, locking them inside. Being an expert with electronics, Gromit manages to break into the trousers' circuits to make them march and eventually break the wardrobe apart. There follows a fast chase aboard a train set, as Gromit attempts to stop Feathers escaping with the diamond. Wallace's attempts to aid are mostly unsuccessful, though he removes Feathers' revolver and frees himself from the trousers. After Feathers' train is abruptly stopped by the trousers, he is captured and handed in to the police station. In the final scene of the film, Feathers has returned home to the zoo and is clinging furiously to the prison-like window bars. For catching Feathers, Wallace and Gromit are given their substantial reward, which pays off their debts. Meanwhile, the trousers, unceremoniously consigned to the dustbin, walk off by themselves into the sunset.