Break up the chicken carcass or bones and put into a large saucepan or stockpot. Add the vegetables, bay leaf and peppercorns. Pour over the water.
Bring to the boil over a high heat, then turn the heat down so the liquid is simmering gently. Cover the pan and leave to bubble for 1 hour.
Strain the stock through a sieve into a bowl, discarding the bones and vegetables. Skim any fat from the surface with a spoon, if using the stock straightaway. Alternatively, chill the stock first, which will make it easier to remove the fat.