Chicken feet are a common delicacy in the Philippines (and I suspect, a lot of other countries). The claws and tips of the toes are cut off, and the feet are washed in hot water and the tough outer layer of the skin is peeled or scraped off.
Chicken feet (or "adidas" in Tagalog slang, from the brand of running shoe) is usually cooked adobo-style.
This produces a thick, jelly-like crust, which is eaten with rice (as are most Filipino viands) or on its own, as a snack.
You generally have to nibble away each toe, one joint at a time, spitting out the bone, but the ball of the foot (what would be the "palm" of an equivalent human hand) is a soft, chewy mass of delicious ligament.
Aside from adobo, chicken feet are used as thickener for soup, as the ligaments dissolve as the feet are boiled, adding a nice gelatinous texture to chicken broth.
Chicken feet will usually only be served in middle-class or lower-class homes, as the rich are too Americanized to even think of serving such fare. The same for food outlets - you'll only see this in the neighborhood carinderia but never in the posher restaurants.