In a large stockpot, combine the chicken parts, onion, celery, carrots, parsley, bay leaves, peppercorns, rosemary, thyme, and water. Bring to a boil over high heat, lower the heat, and partially cover. Cook at a barely bubbling simmer for at least 2 hours or up to 4 hours, occasionally skimming off any scum that collects on the surface.

When the stock has finished simmering, set aside to cool. Strain the liquid through a sieve or cheese-cloth-lined colander into a large heatproof bowl. Let cool slightly, cover, and refrigerate. Discard the vegetables and other solids.

Refrigerate the stock until chilled, then skim off the fat. The stock will keep, refrigerated, in a tightly covered container for up to 3 days. The yield varies according to how long the stock has simmered. Yield: 2 to 2 1/2 quart