Combine the lime juice, vinegar, paprika, bitters and hot pepper sauce in a glass baking dish.
Wearing kitchen gloves, split the jalapeno pepper, remove seeds.
Mash the pepper with the garlic into a smooth paste using a mortar or an electric spice grinder.
Add the paste to the lime mixture in the baking dish and combine.
Toss the chicken pieces and swish them in the marinade until they are completely coated. Cover and let marinate overnight in the refrigerator.
Remove the chicken from the marinade and grill or broil until cooked through and burnished, about 20 minutes on each side. Baste frequently with the marinade. If the chicken looks like it is beginning to burn, move it farther away from the heat source.
Serve hot with chilled orange sections and plenty of napkins.