Look for "stock" (made with bones for more body) rather than "broth" (made with meat) if you want a richer mouthfeel.
Ask for chicken backs, necks, or feet. Many butchers sell these "scraps" cheaply, and they are superior to using a whole chicken for stock. where to buy chicken stock
If you prefer to make your own, you need specific "scraps" that are high in collagen for a rich, gelatinous texture. Look for "stock" (made with bones for more