Preheat the oven to 450 F. Rinse the chicken bones in cold water and place in a large roasting pan. Roast the bones until browned on one side, about 20 minutes. Turn the bones, add the carrots, celery and onion to the pan, and roast until evenly browned, about 20 minutes longer.
Transfer the vegetables and bones to a stockpot. Deglaze the hot roasting pan with a little water, stirring with a wooden spoon to scrape up any browned bits, and add the liquid to the stockpot. Add the peppercorns, parsley and cold water and slowly bring to a boil over medium-high heat. Reduce the heat to low, cover partially, and simmer for 1 1/2 hours, using a spoon to regularly skim off the foam that rises to the surface. Remove from the heat and let cool slightly.
Carefully strain the stock into a bowl through a colander or sieve lined with paper towels or cheesecloth (muslin). Discard the bones and solids. Let cool at room temperature for about 1 hour.
Cover and refrigerate the stock overnight. With a large spoon, lift off any solidified fat from the surface and discard. Use the stock immediately, cover and refrigerate for up to 2 days, or freeze in airtight containers for up to 3 months. Makes about 12 cups.