In a large dish, mix the olive oil, vinegar, lime juice, sugar, thyme, allspice, cinnamon, salt, and cayenne pepper. Stir in the scotch bonnet pepper, green onions, and garlic. Pierce chicken on all sides with a fork, and place in the dish. Cover, and marinate up to 24 hours in the refrigerator, turning occasionally.
Preheat the grill for high heat.
Lightly oil grill grate. Discard marinade, and grill chicken 8 minutes on each side, or until juices run clear.