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. 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.
Mrs. Tweedy realises 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. Soon, a Rhode Island Red rooster appears to fly over the fence and crash into the coop. The hens fawn over the new arrival, Rocky, and keep him hidden from the Tweedys. 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 realises they can build a plane from Fowler's pictures and personal recollections. The chickens 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 axe. Rocky, having had a change of heart, 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 after losing the pair of scissors, tricks Mrs. Tweedy into using the hatchet to severe the string. Mrs. Tweedy ends up crashing into the pie machine, plugging up a the safety valve and causing it to explode, destroying the barn. The chickens cheer and continue flying to safety as Mr. Tweedy, who reminds his wife, "I told you they was organized, untill she gets crushed and killed by the door.
The film concludes with the chickens having found an idyllic setting in a 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 starting their own chicken farm so they can have all the eggs they could eat, but then end up arguing over whether the chicken or the egg came first