In a small bowl, combine the marinade ingredients, adding salt and pepper to taste.
Put the chicken pieces into a bowl with the marinade. Cover and refrigerate for at least 3 hours, turning the chicken pieces occasionally. Drain and discard the onions and parsley.
Heat the oil in a sauté pan over medium heat. Add the onions and garlic, and sauté for about 2 minutes, or until the onions begin to soften.
Add the chicken pieces, salt and pepper, to taste, and cook for about 5 minutes, turning occasionally. Add the lemon juice and lime sections, then turn up the heat to bring the liquid to a boil. Cover and lower the heat to a simmer. Simmer for 20 minutes.
Remove the chicken pieces and keep warm. Add the buttermilk or cream over low heat and heat through.
Put the chicken pieces back into the sauce and turn to coat. Place 2 pieces of chicken on each plate. Garnish with the parsley and lime slices, if desired.
Recipe reprinted by permission of Doubleday. All rights reserved.