The Tweedys are a middle-aged couple who run a struggling chicken farm in Yorkshire, England. Mrs. Tweedy (voiced by Miranda Richardson) is the malicious brains of the pair, while Mr. Tweedy (voiced by Tony Haygarth) is dim-witted, but suspects the chickens are trying to organise. 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. Their unofficial leader Ginger (voiced by Julia Sawalha) has attempted numerous escapes, often using 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 thrown into a coal bin for solitary confinement. Ginger is released from the bin just in time for roll call the next day, when Mrs. Tweedy removes one chicken called Edwina who has laid no eggs for a week and slaughters her for 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 rally the other chickens' spirits so they will speed up their efforts to escape. However, she soon concludes that their only viable plan is to go over the fence, something that has not been tried yet. As she stands outside the coop that night, she sees a Rhode Island Red rooster named Rocky (voiced by Mel Gibson), who hurtles over the fence and crash-lands in the coop. The other chickens fawn over Rocky, while Ginger finds a torn section of a poster that appears to show Rocky flying. 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 in the crash. 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.
The chickens are surprised by a large piece of equipment being delivered to the farm, followed by Mrs. Tweedy's order to double their feed rations. Ginger concludes that the Tweedys are trying to fatten the chickens up and then kill them all, leading to an argument between her and Rocky over telling the chickens the truth and not destroying their morale. Discovering that Ginger's news has sent them into a depression, Rocky organises a party using a radio procured by Nick and Fetcher. Rocky's wing has fully healed by now, but before Ginger can persuade him to give a flying demonstration, she is taken by Mr. Tweedy for a test of their new equipment - a machine for making chicken pot pies.
Rocky rescues Ginger from the machine, sabotaging it in the process so that they will have more time to work on their escape. Fowler (voiced by Benjamin Whitrow), an older rooster who has been doubtful of Rocky's acts, now begins to respect him and gives Rocky 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 missing section of his poster, which shows that he was actually a stunt cockerel who "flew" by being shot from a cannon. This revelation outrages and demoralises all the chickens except Ginger. When Fowler arrives to try to 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, paying them with fresh eggs. The chickens race against time to assemble their plane as Mr Tweedy repairs the pie machine.
The chickens complete their plane just as Mr. Tweedy enters the coop to grab them. However, the chickens launch an open revolt by tying up and gagging him. As they are preparing to take off, Mr. Tweedy frees himself and knocks down the launch ramp. Ginger jumps down as Fowler turns the plane around, knocking Mr. Tweedy unconscious. Ginger and Rocky - who returns to the farm after seeing an ad for the Tweedys' pies - set the ramp back in place and climb aboard the plane by grabbing a string of lights hanging from the landing gear. Mrs. Tweedy then manages to grab the end of the string and is dragged into the air, weighing the plane down, and Ginger crawls out to try to cut the string. Mrs. Tweedy swipes at her with her hatchet, but is foiled by Rocky with help from Nick and Fetcher launching the eggs at her. After all the eggs are dispersed, Mrs Tweedy swipes at Ginger again and seemingly beheads her, but soon realizes she has accidentally severed the string, and Ginger lets her fall through the barn and into the pie machine, plugging its safety valve. This causes the machine to build up pressure and explode in a mushroom cloud of gravy covering the entire farm, destroying the barn. Mr Tweedy then reminds his wife for not realizing that the chickens were planning to escape, and after this enrages her further, the barn door (the last standing structure of the barn) collapses on her as the chickens continue their flight to freedom.
In the epilogue, the chickens have established a sanctuary for themselves, where they can live in comfort and raise their baby chicks. Rocky and Ginger begin a relationship, and Nick and Fetcher discuss the idea of starting a chicken farm of their own. During the closing credits, their talk becomes an argument over whether the chicken or the egg came first.