Soak 1 cup hickory wood chips in water for 1 hour; drain well.
Mix together paprika, brown sugar, salt, garlic powder, onion powder, peppers, and cloves. Massage spice mixture onto surface of turkey breast.
Preheat grill over medium-high heat, using both burners. When hot, turn the left burner off, but keep the right burner on. Put wood chips on hot coals. Lay turkey on left side of cooking spray coated grill rack. Shut lid and cook 1 hour and 50 minutes or until a meat thermometer reads at least 180 degrees F, flipping once during cooking.