Place chicken breasts on a platter with raised sides and cover the breasts with oil. Rub both sides with garlic. In a small bowl, mix the dry rub ingredients with a spoon. Dust both sides of the chicken breasts and gently rub the spices against the meat. Lightly cover the chicken with a towel and refrigerate for at least 1 hour.
In a small saucepan, add the butter, rum, brown sugar, can of pineapple bits (with juice), and Worcestershire sauce. Add a dash of red pepper flakes. Bring to a mild boil over medium-high heat and continue to stir and heat for 10-15 minutes. Remove from heat and allow this to cool and thicken for 30 minutes.
Prepare outdoor grill. One side of the grill should be high, other side medium. Clean the grates with a wire brush and coat well with vegetable oil using a balled paper towel or aluminum foil.
Adjust the high heat side down to medium, with the other grilling surface to low. Place the thickest part of the breast over the medium heat side of the grill on a 45 angle to the grate. [Facing 10 on a clock]
Grill for 5 minutes (if more than 1 thick). Turn the chicken over and grill for another 4-5 minutes in the same direction or position.
Turn the chicken over once again (this time facing 2 on a clock). Medium heat on the thicker side of the meat. This may require adjusting the flame on a gas grill or moving the grate around on a charcoal grill.
Brush the sauce over the chicken breasts very thick and grill for 2 minutes. Turn the breasts over, keeping within the same direction and brush more sauce on top. Grill for another 2 minutes. Place the chicken on a serving platter and add more sauce. Set aside.
Place the pineapple slices on the grill and cook on both sides for 4 minutes using the sauce. When done, place the slices on a small plate and move them to a cutting board. Slice up the rings into 1 pieces.
Place the chicken breasts on individual plates, add the pineapple pieces, and top this with chopped scallions. Serve with your favorite rice mixture. [Pictured, black beans and rice]
