Cut chicken in quarters and wash in a mixture of vinegar and water.
Combine thyme, escallion, garlic, ginger, onion, jerk seasoning, sugar, pimento berries, whole pepper, soy sauce and rum in a blender. Add 1 1/2 cups water and blend until smooth.
Pour blended seasoning mix over the chicken and rub the mixture in. Cover and put to marinate in the refrigerator for about 1 hour or overnight.
Place chicken on a preheated grill or in an oven 180°C/350°F and cook for about 1 1/4 hours. Turn the chicken pieces so that it develops a brown colour on both sides.
TO MAKE THE SAUCE: Combine ingredients for sauce and put to boil. Pour in the marinade from the chicken, mix well and boil until the mixture thickens. Use to glaze the chicken.
TO SERVE: Chop each quarter in 2-4 pieces and serve with roast sweet potato, breadfruit, slices of bread or with boiled rice.