Place the chicken in a stock pot. Pour in enough water to cover. Bring to a boil and for the first 15 minutes, skim off any foam that comes to the surface. Add in the carrots, celery, onion, bay leaves, dill, salt and pepper. Simmer for 2-3 hours, slightly covered.
Strain soup into another stock pot and skim off any fat. Return vegetables to the sauce pan and add the parsley and peas. Chop the meat off the chicken and add that to the soup as well. Serve when peas are cooked through.