Measure water into a large soup pot and add all the ingredients. Slowly bring to a boil over medium heat, then immediately reduce the heat and simmer for 3 hours, using a spoon to frequently skim the soup as well as possible. Remove from heat and cool. Skim fat from the surface and strain the soup. Wash out the soup pot and return the strained stock to the pot.
Remove and discard bay leaf and parsley. Mash the carrots, celery, and garlic and stir them into the soup. Remove the skin and bones from the chicken, chop the meat and add to the soup. (If the chicken meat has completely fallen apart, that's ok, too; just use as is, with bones removed.) Heat and season to taste with additional salt and pepper.