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Season chicken evenly with Rub. Refrigerate 30 minutes, if desired.
Prepare grill for indirect medium-low heat (250°F to 325°F). Preheat grill by turning all burners to high with lid closed. Turn off burner(s) on one side of the grill. Turn burner on the other side to medium-low. Place chicken on unlit side of grill. Close lid.
Note: To maintain medium-low heat (250°F to 325°F), keep lid closed and adjust lit burner as necessary. Directions were developed using a gas grill. Grills vary; cooking time is approximate.
Grill 40 to 45 minutes or until internal temperature of thickest part of chicken is 165°F, turning occasionally. Move chicken to lit side of grill with skin-side down. Turn lit side of grill to high.
Grill, uncovered, 3 to 5 minutes longer or until chicken is lightly charred, turning once and brushing with BBQ sauce if desired.