Chicken Run is a true clay model stop-motion animation; made by Aardman Animations.
They came from almost nowhere [they had history but weren't well-known in their own right*] with a series of adverts for UK television, extolling the benefits of gas central heating. Each advert featured a vox pop of a real interview, with an clay stop-mo animal taking the visual part.
This was eventually turned into a show in its own right, called Creature Comforts, which won an Oscar.
They then made the short film starring Wallace & Gromit, A Grand Day Out, which failed to win the oscar because it was beaten by Creature Comforts, followed by two more shorts, The Wrong Trousers & A Close Shave. Then they moved to a full-length feature, The Curse of the Were-Rabbit. All three were Oscar-winners.
*Their most famous earlier contributions were for the BBC TV show Vision On & the video for Peter Gabriel's Sledgehammer, where they also stop-mo'd Gabriel as well as the backgrounds.