Rinse the chicken, cut up the vegetables, and cover all of the ingredients with cold water, about 2 quarts. Simmer gently for about 2 hours, skimming occasionally. Strain the stock, cool, and remove any fat. This stock will keep in the refrigerator for 3-4 days, or it may be frozen.
Or, of course, you can use the leftover bones of a roast or fowl as the base of your stock. Here are some hints for soup-making from turkey, duck, or goose bones.