Heat barbecue to medium-high. Combine the first 7 ingredients in a small bowl. Cover and refrigerate
Brush the chicken with the oil; season with salt and pepper. Turn the heat off on one side of the barbecue. Place chicken, skin-side up, on that side of barbecue. Close the lid and cook the chicken until cooked through, about 30 minutes, or until the temperature in the deepest part of the breast registers 170 degrees F on an instant read meat thermometer. When done, set the chicken skin-side down on the hot side of the barbecue and cook 1 to 2 minutes to richen its colour. Set the chicken skin side up, and baste with barbecue sauce. Let the sauce heat through a few minutes and serve.