To make basil pesto- Combine basil, garlic, and pine nuts in a food processor and pulse until coarsely chopped. Add 1/3 cup of oil and blend until smooth. Season with salt and pepper. Stir in the cheese and set aside.
Preheat the oven to 450 degrees. Spread pesto sauce over the pizza crust evenly. Arrange chicken pieces and artichoke hearts over the sauce. Top with mozzarella cheese.
Bake for 10 minutes or until the cheese has melted and flatbread is browned and crispy.