Preheat oven to 425°F.
In a small saucepan over medium-low heat, combine the alfredo sauce and half of the Cooper cheese. Stir consistently until cheese is melted.
Place the pizza crust on a baking sheet. Spread the alfredo cheese sauce mixture evenly over the crust to within 1/2 inch of the edge. Break apart the remaining cheese (shredding it) and sprinkle over the sauce. Top with chicken, red onions, tomatoes, and fresh basil.
Bake for 15-20 minutes or until the crust and cheese are golden brown.