Marinade: In a small bowl whisk together brown sugar, vegetable oil, fresh orange juice, lime juice, garlic, dried thyme, minced ginger, rum extract, allspice, cayenne, black pepper and bay leaves.
Pour over the chicken breasts. Place into a one gallon size plastic storage bag or shallow dish and chill. Marinate for 4 hours or overnight.
Grill: Remove chicken from the marinade and discard the marinade.
Oil the grates of a gas grill and preheat to medium high heat. Grill the chicken breasts over medium-high heat for around 5 minutes on each side or until the juices run clear.
Let the chicken rest for 5 minutes, before carving and serving.
Serve with a generous drizzle of the sweet and spicy glaze on top.
Honey Rum Glaze: Stir all of the ingredients together reserving the rum extract. Warm in the microwave for 25-35 seconds. Stir in the rum extract.
Drizzle over the chicken before serving. (The glaze easily doubles.)