Season chicken with 3 tablespoons of the Applewood Rub. Refrigerate 30 minutes, if desired.
Mix mustard, vinegar, water and remaining 2 tablespoons of Applewood Rub in medium bowl until blended. Set aside.
Prepare grill for indirect medium-low heat (275°F to 300°F). Preheat grill by turning all burners to medium. Turn off burner(s) on one side. Place chicken on unlit side of grill. Close grill.
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. Brush with mustard barbecue sauce. Turn lit side of grill to high.
Grill, uncovered, 3 to 5 minutes longer or until chicken is charred, turning once and brushing with additional sauce.