Light grill before beginning preparation (gas or coals). Melt butter and combine butter, parsley, and Italian Seasoning in a mixing bowl, beating until well mixed. Press ground pepper and salt into chicken's meaty side. On the same side of the chicken, apply a third of the butter and season mix with a basting brush.
When grill is preheated, place chicken and bacon on grill, seasoned side up. Grill chicken for 6-8 minutes, while applying the remainder of the butter mix with a basting brush. Remove the bacon when brown.
Sprinkle the warm chicken with parmesan cheese, then mozzarella. When bacon cools, chop into fine pieces, and sprinkle on top of the chicken. Serve immediately.