Preheat broiler and adjust rack to be about 6 inches from the heat.
Cut or pound chicken into thin slices, about ½-1 inch thick. Set aside in large bowl. Cut onion into large slices. Add to large bowl and mix with chicken.
In a small bowl combine and mix together garlic, ginger, allspice, paprika, thyme, cayenne pepper, and sugar. Add olive oil to form a paste. Pour mixture over chicken and onions and mix to coat evenly (I use my hands).
Arrange chicken and onions on a large broiling or baking sheet in a single layer. Salt and pepper to taste.
Cook under the broiler until chicken is fully cooked (internal temperature of 165 degrees F), about 12-16 minutes. Serve immediately. Suggested sides include: rice, beans, fried plantains, and lime slices.