If necessary, peel away and discard any yellow membrane that adheres to the chicken feet, then chop off the claws. (The process of defeathering chickens often removes that yellow membrane; however, if it remains, it — and the talons — can create off flavors in the broth.)
Combine the chicken feet, onion, celery, carrots, peppercorns, thyme, parsley, bay leaves, and wine in a large, heavy stockpot.
Cover the chicken feet and other ingredients with the water.
Bring to a boil over medium-high heat, then immediately decrease the heat to medium-low, cover, and simmer for 8 to 12 hours, adding water as necessary to keep the feet submerged. From time to time, skim away any scum that might rise to the surface.
Strain the broth, discarding the solids, then pour it into jars, cover, and store it in the refrigerator for up to 1 week or freeze it for up to 6 months.