Divide the sauce for grilling, and serving.
Set up your grill for indirect smoking.
Set aside half the Alabama sauce, about 1/3 cup-to use as a finishing sauce. Slow smoke your chicken for a good 2 hours, brushing lightly with the sauce now and then. You'll want to smoke it until the juices run clear when its pierced to the bone and/or an instant read thermometer reads 180F.
Spoon a tablespoon of the reserved sauce over each serving.
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