Lightly fried chicken simmers away in a spicy Jamaican-style sauce full of tomatoes, onions and Scotch bonnet peppers.
Rinse the chickens and pat them dry with paper towels. Cut the chickens into serving pieces. To make a quick broth, if desired, place the chicken backs, necks, and wing tips into a small pot and cover with water. Bring to a boil, reduce the heat to low, and simmer until needed.
Place the other chicken pieces in a large bowl and squeeze the limes over them, coating each piece with juice. (Leave the lime rinds in the bowl.) Sprinkle on the salt and black pepper, add the onions, tomatoes, garlic, thyme, and Scotch bonnet peppers, and mix well. Set aside to marinate for at least 15 minutes and up to an hour.
In a large skillet, heat half of the oil over high heat until it is very hot. Fry half the pieces of chicken until golden on both sides, about 5 minutes per side. Remove the pieces from the pan and set aside on a large plate. Wipe out the old oil and add the remaining oil. Repeat the frying process with the rest of the chicken pieces. Remove the chicken from the pan and pour out the oil. Discard the lime rinds from the tomato mixture. Return the pan to medium-high heat, add all the chicken pieces and tomato mixture, and cook, stirring for 3 minutes. Blend in the water or chicken stock. Reduce the heat to medium-low, cover, and simmer until the chicken is tender, 40 to 45 minutes. Remove the whole Scotch bonnet pepper. Serve the chicken with the sauce spooned over it.