To a Dutch oven or large stock pot, add chicken and cold water to cover (see note 3).
Over medium-high heat, bring to a boil. Immediately reduce heat to low and skim the foam off the top.
To the pot add onion, carrot, celery, and salt. If desired, tie parsley stems, thyme, garlic, bay leaf, and peppercorns to make a sachet or add loosely to the pot (see note 5).
Simmer gently (bubbles should barely break the surface at irregular intervals) until the chicken is cooked through, at least 1 hour or up to 5 hours. The longer the broth simmers, the more flavor it will have. (NOTE: After 1 hour, you should remove the chicken breasts from the pot to prevent them from drying out).
Remove chicken from pot to a rimmed baking sheet or large bowl. Separate chicken, discarding skin and bones (you should have about 4 cups chicken).
Strain the broth through a fine-mesh strainer or cheesecloth. Place in a large bowl and chill covered overnight in the refrigerator.
The next day, scrape off the accumulated fat from the top of the stock and discard. Divide the broth into freezer-safe containers (leaving at least ½-inch for expansion), label, and freeze. Or, refrigerate and use within 4 days.
