Prep the chicken. Rinse and pat dry. If you prefer a cleaner broth, remove the skin.
For deeper flavor, keep it on. Cut large pieces so they're roughly uniform for even cooking.
Optional: Parboil for clarity. To get a clear, clean broth, place chicken in a pot, cover with cold water, bring to a boil for 2 minutes, then drain and rinse. This step removes foam and extra fat.
Build the base. In a large pot, add chicken, sliced onion, garlic, peppercorns, bay leaves, and the whole Scotch bonnet (if using).
Pour in 6–8 cups of water to cover by about an inch.
Simmer gently. Bring to a boil, then reduce to a gentle simmer. Skim any foam. Cook uncovered for 20 minutes, seasoning with 1 teaspoon salt.
Add vegetables. Stir in potatoes, celery, and carrot.
Continue simmering 20–25 minutes more, until the chicken is tender and the potatoes are just soft but not falling apart.
Brighten the broth. Remove the Scotch bonnet if you used it and want only mild heat. Stir in lime juice and vinegar (if using). Taste and adjust salt and acidity.
You want a tangy, lightly salty, peppery balance.
Finish and serve. Add a few sprigs of fresh herbs for aroma, then fish them out before serving. Ladle into bowls and serve hot. Many people enjoy it with buttered toast, johnny cake, or a slice of bread for dipping.