Place chicken parts in a stockpot just large enough to hold them with about 3 inches of room above (an 8-quart pot should do), and add enough water to cover by 1 inch (about 3 quarts). Bring to a boil over medium-high heat, using a ladle to skim impurities and fat that rise to the top.
Add vegetables, bay leaf, and peppercorns, and reduce heat to a bare simmer (bubbles should just gently break the surface). Cook, skimming frequently, for at least 1 1/2 hours and up to 4 hours.
Pass the stock through a cheesecloth-lined sieve into a large heatproof measuring cup or another bowl or pot; do not press on solids. Discard solids.
Skim off fat if using immediately, or let cool completely (in an ice-water bath, if desired) before transferring to airtight containers. Refrigerate at least 8 hours to allow the fat to accumulate at the top; lift off and discard fat before using or storing stock. The stock can be refrigerated up to 3 days or frozen up to 3 months; thaw completely in the refrigerator before using.