Blend ingredients for jerk sauce, make sure to reserve ⅓ cup.
Using asharp knife, make a series of deep cuts into the chicken. This will help the jerk sauce to penetrate the meat. Place the chicken in a sealable bag and pour jerk sauce over top of the meat. Remove as much air as possible and massage the sauce into the chicken. Place on a plate and put in the refrigerator for a minimum of two hours, but preferably overnight.
For the glaze, add oil and molasses to reserved jerk sauce, mix together and place in an airtight container. Leave on the counter until the chicken comes off of the grill.
Set your grill up for high direct heat, usingoak woodorcharcoalin the grill drawer. Once coals are ashed over and the grill grate is preheated, place the chicken on the grill over high direct heat. Wearingheat-resistant glovesand using along set of tongs, flip the chicken often to ensure even browning (but not burning) on all sides.
Continue grilling until the chicken reaches an internal temperature of at least 165°F. Remove chicken from the grill, dress with glaze and serve hot.