In a stock pot over medium-high heat, combine the chicken, water, chicken stock, onion and barley. Bring to a boil, and then reduce heat to low and simmer for 1 hour. Remove chicken, discarding the bones and skin, chop meat into bite size pieces and return to the pot. Add the leeks, celery, thyme, parsley, salt and pepper. Simmer for 30 more minutes, or until all vegetables are tender.