Most chickens sold in American supermarkets are slaughtered when very young and tender, to provide the greatest possible versatility in cooking. The only problem with this practice is that the birds are rather bland, because they haven't lived long enough to develop a strong chicken flavor. That's not the case with stewing chickens -- larger older hens and roosters that have lived long, full chicken lives. Although they're too tough for many popular recipes, their rich flavor makes them perfect for soups and stews.
Place the chicken in a large pot, and cover it with cold, fresh water. Bring it up to a simmer, not a boil, and simmer for 15 minutes. Skim away the grey protein film that rises to the surface, and pour out the water. This process, called blanching, is optional but makes your broth clearer.
Fill the pot again with cold, fresh water, and bring it back up to a simmer. Add one coarsely chopped large onion, two sliced ribs of celery, one diced carrot, one bay leaf, and 10 to 12 whole peppercorns.
Simmer the chicken until it's tender, usually 1 to 1-1/2 hours depending on the size and toughness of the bird. Remember: the older and tougher the bird, the better the flavor.
Remove the chicken from the broth, and peel the meat from the bones once it's cool enough to handle. Return the bones, skin, neck and wingtips to the pot, and continue simmering for another hour. Cover the deboned meat, and refrigerate it.
Strain the broth, and pour it back into the pot. Taste the broth; it should have a rich chicken flavor. If it doesn't, simmer it for another hour until it's reduced by 1/3, and taste it again. Season with salt and pepper when it's ready.
Use the meat in your favorite recipes, and portion and freeze the broth for later use. Alternatively, add diced vegetables and noodles to the broth to make soup, and add diced chicken at the last minute.