1. Preheat oven to 500°.
2. Heat oil in a medium skillet over medium-high heat; sauté peppers for 2 minutes. Set aside. Roll out pizza dough to a 15-inch round on a lightly floured surface; top with cheeses and sautéed peppers. Transfer to a baking pan. Bake pizza for about 12 minutes or until crust is golden brown.
3. Meanwhile, warm up chicken. Toss warm chicken pieces with barbecue sauce. Remove pizza from the oven; evenly arrange chicken on top. Sprinkle with salt and pepper, and top with parsley. Cut pizza into slices; serve.