The Tweedys are a grumpy middle-aged couple who run a chicken farm in Yorkshire, England. The coop is run in the style of a World War II prisoner of war camp, with the chickens accountable for the number of eggs they lay each day or else face being on the chopping block. Any hen that ceases to produce eggs is slaughtered for food. One chicken, Ginger, has attempted numerous plans to flee the coop, aided by contraband smuggled into the coop by two rats, Nick and Fetcher, but she is always caught by Mr. Tweedy and his dogs, and placed into solitary confinement. However, Ginger is released just in time for roll call the next day. Ginger faces problems with two black-marketer rats named Nick and Fetcher who are tired of being payed with chicken feeds, wanting anything can be better.
Mrs. Tweedy realizes her farm is failing and reads a catalogue on products to increase the profits. Ginger tries to convince the other hens to speed up their efforts to escape, but soon comes to conclude the only escape route is to go over the fence, something chickens cannot do. While thinking of a new plan, Ginger observes an American Rhode Island Red cockerel flying over the fence and crash into one of the coops, spraining his wing. Ginger and the other chickens help to hide him from the Tweedys and care for his wing, learning that his name is Rocky. Ginger finds part of a poster Rocky dropped, claiming that he can fly. She tries to convince Rocky to help them escape by teaching them how to fly, but Rocky's wing was injured and cannot show them immediately. Instead, he puts them through a set of exercises that seem to have no purpose while assuring the chickens they are making progress. Soon, the Tweedys have machinery delivered and begin assembling it. At the same time, Mrs. Tweedy orders food rations doubled, intending to fatten the chickens up! Ginger is the only one to take serious note of this.
Soon, what is revealed to be a pie machine is completed, and Mr. Tweedy grabs Ginger for its first test. Rocky rescues Ginger, and they manage to jam the machine, giving them more time to work out their escape. Fowler, an older rooster, gives Rocky his respect for saving Ginger, giving him his old RAF badge in tribute. Rocky decides to flee the farm the next day. Ginger finds Fowler's medal and the second part of the poster, showing that Rocky was a stunt rooster, "flying" by being shot out of a cannon. This revelation shocks the chickens, and a fight soon breaks out as morale falls. When Fowler arrives to restore order and begins talking of his days in the Royal Air Force, Ginger realizes they can build a plane from Fowler's pictures and personal recollections. The chickens, with Nick and Fetcher's help, race against time to assemble the aircraft while Mr. Tweedy works to repair the pie machine.
The chickens finish their machine just as Mr. Tweedy completes repairs and enters the coop to grab the chickens. Led by Ginger, the chickens launch an open revolt, tying up and gagging Mr. Tweedy and readying the "crate". As they prepare for take off Mr. Tweedy breaks himself loose and knocks down the ramp. Ginger jumps down while Fowler turns the plane around, knocking Mr. Tweedy unconscious. As Ginger struggles to lift the ramp, Mrs. Tweedy arrives with an earlier used hatchet. Rocky, (who had seen the billboard advert of chicken pies), flies in over the fence and hits Mrs. Tweedy. Ginger and Rocky grab onto a string of lights caught on the plane's landing gear- Mrs. Tweedy soon wakes up and now in a burst of primal rage grabs onto the lights too, weighing down the crate. Ginger heads down the string to cut it, but Mrs. Tweedy crashes into her own billboard, the impact had sent Ginger out of the crate and onto the string. Just as Mrs. Tweedy swipes at Ginger with her hatchet but is foiled by Rocky launching eggs at her with the help of Nick and Fetcher which causes Mrs. Tweedy to accidently make Ginger to lose the pair of scissors, Ginger tricks Mrs. Tweedy into using the hatchet to severe the string. Mrs. Tweedy ends up falling through the barn and crashing into the pie machine, plugging up a the safety valve, this causes the machine to build up pressure and explode in a mushroom cloud of gravy which floods the entire farm, destroying the barn leaving only what's left of the barn and the barn door standing. Mr. Tweedy (who isn't covered in gravy and was standing behind the door), who reminds his wife, "I told you they were organized", which only enrages her further. Having enough, Mr. Tweedy then pushes the door on to of her which leads to her getting crushed and killed as the chickens cheer and continue flying to freedom.
The film concludes with the chickens having found an bird sanctuary where they can live in comfort and raise their new chicks, while Ginger and Rocky fall into a romantic relationship. Meanwhile, Nick and Fetcher discuss about starting their own business in cooking, while arguing over whether the chicken or the egg came first.