Combine marinade ingredients and mix well. Trim excess pieces of fat from thighs, but leave a majority of the skin on. Place thighs in a resealable plastic bag. Pour marinade over top making sure all meat surfaces are coated. Seal bag and turn to coat. Refrigerate for 3-6 hours.
While chicken is marinating, prepare the barbecue sauce. Add all ingredients, except butter, to a medium saucepan. Bring to a simmer over medium-high heat for 1 minute. Stir often. Reduce leat to low heat and let the sauce simmer for an additional 5 minutes. Add butter an simmer for an additional 1-2 minutes until it has dissolved. The sauce should be rich and silky.
If making the sauce a day in advance, cool completely and store in an airtight container in the refrigerator. Rewarm sauce in microwave or stove top. Do not boil or overheat, just bring back to room temperature before using.
Remove chicken legs from the bag and discard marinade. Place chicken thighs on preheated grill over medium-low heat (around 300 degrees or 150 degrees C). Grill for roughly 30 minutes with the lid down; turning occasionally. Once the chicken reaches an internal temperature of 155 degrees F., begin brushing sauce over the surface every 5 minutes until chicken is done, and the sauce has a sticky appearance. Remember, the chicken is fully cooked when the meat has reached an internal temperature of 175 degrees Test more than one piece for consistency.
Place cooked chicken onto a large platter. Tent with aluminum foil and let rest for 5-7 minutes before serving.