Preheat the oven to 375 degrees F (190 degrees C).
In a small bowl, mix together the butter, olive oil, garlic, pesto, basil, oregano, Parmesan cheese and Alfredo sauce. Arrange the chicken on top of the pizza crust. Pour the Alfredo sauce mixture evenly over the chicken. Top with tomato and feta cheese.
Bake for 10 to 15 minutes in the preheated oven, until the crust is lightly browned and toppings are toasted. Cut into wedges to serve.