Rub chicken generously with Stubb's BBQ Spice Rub. If using breasts with skin on, be sure to put some rub under the skin so that the flavor absorbs into the meat. Let it rest for 15 minutes before cooking.
Grill for 1-1 ½ hours over indirect heat, basting with Stubb's Moppin Sauce every 15-20 minutes while cooking (you can adjust how often you baste according to your taste). When cooking over indirect heat, no flipping of the meat is required.
Once the chicken is cooked to 165 degrees, serve with plenty of Stubb's Bar-B-Q Sauce.