Heat oven to 450° F and line large baking sheet with parchment paper.
In large skillet over medium heat, heat 1 tablespoon oil. Add onion, garlic and mushrooms, and cook, stirring frequently, 10 minutes, or until onions are soft. Reserve.
Roll pizza dough into thin oval on lightly floured surface. Transfer to prepared baking sheet and brush lightly with olive oil then spread evenly with Alfredo sauce.
Top with mushroom mixture, cheeses, chicken and rosemary. Sprinkle olives over pizza.
Bake 10-15 minutes, or until cheese is melted and lightly browned around edges.
Serve with Parmigiano-Reggiano.