To prepare the white sauce, combine all of the ingredients in a bowl or mason jar. Stir to combine and refrigerate for at least 30 minutes before using.
To make the chicken, preheat the grill to 400 degrees.
Coat the chicken in the barbecue dry rub. Place the chicken on the grill and cook for 3 minutes.
Turn and brush with the white sauce. Cook for 3 more minutes. Turn and brush with the sauce again.
Continue turning and coating every 3 minutes until the chicken is cooked through, about 10 minutes total.
Serve the extra sauce on the side.
Notes
Be sure to place the sauce you'll be using for basting in a small bowl. Do not dip the basting brush into the full container of sauce or it will become unusable due to the raw chicken.