In "Show No. 306", after the "Scenes Cut From a Movie" sketch, Drew tells Colin that his Scottish accent sounds less like Mel Gibson in Braveheart and more like "the woman from Chicken Run."
During the "Hats" segment of "Show No. 319", Wayne puts on a chicken hat and claims that his "lovin's so good, it'll make your chicken run. See, it's a movie!"
The Muppets: In "Little Green Lie", Rizzo comments that he thinks Camilla said something about her and Gonzo staying home to watch Chicken Run again (actually, she said that they would watch Logan's Run).
In the Hilarious Outtakes for Welcome to... Fanfiction.Net!, Jello says that the best way to make characters likable is to make them chickens and brings up the movie, which he accidentally calls Chicken One.