Prepare the marinade by mixing all ingredients in a bowl. Put the chicken in a bowl and pour in the marinade. Toss lightly to coat. Cover and let marinate in the refrigerator for at least 1 hour or overnight, if possible.

Prepare a medium-hot fire for grilling, or preheat a gas grill and place the rack about 3 inches from the source of heat. Brush the grill with olive oil and arrange the chicken on top. Cover and cook 12 to 13 minutes per side, if using legs and thighs. To test for doneness, pierce the thickest part of the meat with a sharp knife; the juice should run clear. Serve with mango salsa and a side vegetable.