Preheat oven to 450°F. Heat oil in a frying pan and add onion and pepper strips. Fry over medium heat until soft, adding a little water instead of more oil if onion and pepper start to burn.
Add chicken and barbecue sauce. Stir and remove from heat. Place ready-made crust on cookie sheet. Spread chicken, onion, and pepper mix evenly on crust. Top with mozzarella. Bake for 10 minutes, watching carefully that cheese doesn't brown too much.