For the rub: Mix all ingredients together in a bowl.
For the mop: Mix ingredients in a saucepan, heat to simmer.
Arrange chicken in a single layer on a baking sheet. Season chicken with salt and pepper. Sprinkle rub on both sides of chicken. Prepare grill for medium-high indirect cooking. Scatter drained Alder wood chips over coals. Place chicken, skin side down, on cooking grate on side opposite coals. Cover grill and cook chicken, turning and mopping every 10 minutes, about 35 to 45 minutes or until done.
Bring remaining mop sauce to a low simmer and serve with chicken.