"Logan's Chicken Run"

From Wiki and Wiki:

In the year 2274, the Tweedys are a troubled middle-aged couple who run their own chicken farm in a sealed domed city, a utopia run by a computer that takes care of all aspects of their life.

The city is run in the style of a World War II POW camp, with the chickens accountable for the number of eggs they lay daily. The chickens live a hedonistic lifestyle but understand that in order to maintain the coop, every resident when they reach the age of 30 must undergo the ritual of "Carrousel" [sic] where they are vaporized and ostensibly "Renewed."

To track this, they are implanted at birth with a Lifeclock crystal in the palm of their hand. Edwina's clock turns red and she is beheaded and is later cooked for the Tweedys' dinner.

One chicken, Ginger (voiced by Julia Sawalha), who is often treated as the chickens' leader, has attempted numerous escapes, goes into hiding to avoid Carrousel. She is aided a pair of runners named Logan 5 (Michael York) and Francis 7 (Richard Jordan). Ginger becomes increasingly desperate to find a plan of escape which will work but faces problems after terminating Mr Tweedy.

That same night, as Ginger sits outside of the coop, she  finds an ankh among their possessions. Later, they meet Jessica 6 (Jenny Agutter), a girl also wearing an ankh pendant. A Rhode Island Red cockerel named Rocky (voiced by Mel Gibson), takes the ankh to the computer, where he is told it is a symbol for a secret group who helps the Runners find "Sanctuary".

Mrs Tweedy soon realises that the couple's farm is failing and instructs Logan to find Sanctuary and destroy it. It then changes the colour of his Lifeclock to flashing red, four years early. In order to escape Carrousel herself, Ginger is now forced to become a Runner.