Trim and wash the leeks and shred the white part. Scrub and slice the celery stalks, peel and chop the carrots and onion. Melt the butter in the base of a large pan. Add the prepared vegetables and cook gently until the vegetables are tender but not brown.
Place the chicken on top of the vegetables and add sufficient water to cover. Add a good seasoning of salt and pepper and a bouquet garni. Bring up to the boil, then cover and simmer gently for 45 minutes-1 hour or until the chicken is tender.
Lift the chicken out and allow to cool for a few moments. Peel away the skin and lift the flesh from the bones. Arrange the chicken flesh in a warm serving dish and keep hot while preparing the sauce.