To prepare the barbecue sauce: combine the first 6 ingredients in a medium bowl.
Place 3/4 cup sauce in a large bowl; cover, and chill the remaining barbecue sauce.
Add the chicken legs and thighs to the sauce in the large bowl; toss to coat.
Cover, and marinate in the refrigerator for 8 hours, or overnight.
Set oven to 375 degrees.
Remove the chicken from the fridge.
Place the chicken on a broiler pan coated with cooking spray; reserving the marinade from the bowl.
Bake at 375 for 30 minutes.
Turn the chicken; baste with reserved marinade.
Bake an additional 20 minutes, or until the chicken is done, and discard the marinade On top of the stove, bring the 3/4 cup of the reserved marinade from the fridge to a boil in a small saucepan; reduce heat, and cook until slightly thickened to about 1/2 cup (this should take about 5 minutes).
Drizzle the hot chicken with the sauce before serving, or serve the sauce at the table.