Preheat oven to 400°F.
Boil penne noodles until almost cooked (about 2 minutes less than package directions). Drain and set aside.
Pour 1/4 of the alfredo sauce into the bottom of a medium-sized baking dish.
Place raw chicken breasts on top of the sauce in the baking dish.
Pour more alfredo sauce over the chicken, coating completely.
Add the partially cooked penne noodles and frozen broccoli around the chicken.
Cover everything with the remaining alfredo sauce.
Top with shredded mozzarella cheese.
Cover tightly with aluminum foil.
Bake for 40 minutes or until chicken is fully cooked (internal temperature of 165°F).
Season with salt and pepper to taste before serving.