The Tweedys are a troubled middle-aged couple who run their own chicken farm somewhere in a town in Yorkshire, England. Mrs. Tweedy (voiced by Miranda Richardson) is the ill-tempered brains of the pair, while Mr. Tweedy (voiced by Tony Haygarth) is slow, but he can handle the manual work industriously. The coop is run in the style of a World War II POW camp, with the chickens accountable for the number of eggs they lay daily. One chicken, Ginger (voiced by Julia Sawalha), who is often treated as the chickens' leader, has attempted numerous escapes, which she was aided by contraband smuggled in by a pair of rats named Nick and Fetcher (voiced by Timothy Spall and Phil Daniels). However, Ginger is routinely captured by Mr. Tweedy and his dogs and is later thrown into a coal bin for solitary confinement. Ginger is released from the coal bin just in time for roll call the next day. Mrs. Tweedy soon finds out that one chicken named Edwina had not laid any eggs that week. Edwina is beheaded to death and is later cooked for the Tweedys' dinner. Ginger becomes increasingly desperate to find a plan of escape which will work but faces problems with Nick and Fetcher, who are tired of being paid with chicken feed and want their own eggs instead.
Mrs. Tweedy soon realises that the couple's farm is failing and reads a catalogue on an ambiguous method of increasing profits. Realising something is wrong, Ginger attempts to convince herself and the other chickens to speed up their efforts to escape. However, Ginger soon concludes that the only escape route is to go over the fence and something that she and the other chickens cannot do. That same night, as Ginger sits outside of the coop, she sees a Rhode Island Red cockerel named Rocky (voiced by Mel Gibson), who flies over the fence and accidentally crash into the coop. The other chickens also fawn over Rocky, while Ginger finds the first half of a poster with a picture of Rocky on it that appears to show that he can fly. After Ginger discovers that Rocky is from a circus, she agrees to hide him from his owners if he teaches them how to fly. Rocky reluctantly agrees, but says he cannot show them immediately because he injured his wing when he crashed into the chicken coop. Instead, Rocky puts Ginger and the other chickens through a set of exercises that seem to have no purpose, while assuring them that they are making progress.
Suddenly, a large pie-making machine arrives at the farm, in which Mrs. Tweedy orders all food rations doubled. Ginger proclaims that their intent is to fatten them up and then kill them. Rocky and Ginger argue with each other, which Rocky claims that Ginger's honesty will demoralise the chickens, and Ginger refusing to lie to the other chicken. Discovering that the other chickens have gone into depression following Ginger's announcement, Rocky organises a party using a radio obtained by Nick and Fetcher. During the party, Rocky's wing is shown to have healed. Once their pie machine is complete, the Tweedys kidnap Ginger and later subject her to its first test. Rocky follows Ginger into the machine and rescues her by damaging the machine and giving him and Ginger more time to work on their escape. Fowler (voiced by Benjamin Whitrow), an older cockerel who has been doubtful of Rocky's acts, gives Rocky his respect for rescuing Ginger and his old Royal Air Force (RAF) badge in tribute. Rocky decides to flee the farm the next day, leaving behind Fowler's medal and the second half of his poster, which shows that he was actually a stunt cockerel who "flew" by being shot from a cannon. This revelation outrages and demoralizes all the chickens except Ginger. When Fowler arrives to try and restore order, he begins talking of his days in the RAF, leading Ginger to realise that she and the other chickens could fly out after all by using an airplane, built from the chicken coops, modeled after Fowler's pictures and personal recollections and constructed using tools supplied by Nick and Fetcher. The chickens race against time to assemble their plane as the Tweedys work to repair their pie machine.
The chickens finally finish their plane just as Mr. Tweedy enters the coop to grab them. However, the chickens launch an open revolt by tying up and gagging Mr. Tweedy. As the chickens are preparing to depart, Mr. Tweedy frees himself and knocks down the ramp used to get the chickens' plane airborne. Ginger jumps down as Fowler turns the plane around, which knocks Mr. Tweedy unconscious. As Ginger struggles to lift the ramp, Mrs. Tweedy attempt to kill her with her hatchet. However, Rocky, who just returned after seeing a controversial ad for the chicken pies, jumps over the fence aboard his tricycle and hits Mrs. Tweedy in her face, which knocks her senseless. Rocky and Ginger grab onto the string of lights which was caught on the plane's landing gear as the plane departs. However, Mrs. Tweedy soon awakens and also grab the lights, which weighs down the chickens' plane. Ginger heads down the string to cut it and get rid of Mrs. Tweedy, but she accidentally loses her own scissors. Realising that it is the only way to cut the lights, Ginger manages to trick Mrs. Tweedy by using her hatchet to sever the string, which later causes Mrs. Tweedy to fall, crash into the pie machine, and plugging herself into the safety valve. The pie machine build up its pressure and explodes, destroying the barn, and covering the entire farm with gravy. The chickens continue to fly to freedom as Mr. Tweedy tells Mrs. Tweedy: "I told you they was organised". Mr. Tweedy later pushes the door on top of Mrs. Tweedy before she can lash on him.
In the epilogue, the chickens are happily living in their bird sanctuary, where they can live in comfort and raise their new chicks. Rocky and Ginger fall in love with each other and later become a couple. Meanwhile, Nick and Fetcher discuss their plans of starting their own chicken farm, so they can have all the eggs they could eat. However, Nick and Fetcher ends up arguing with each other over whether the chicken or the egg came first during the film's closing credits.