Prepare the penne pasta according to the package instructions. Drain and rinse under cool water, then set aside.
In a large mixing bowl, combine the cooked pasta, shredded chicken, Italian seasoning, ½ cup of the mozzarella, ½ cup of the Parmesan, and the marinara sauce. Stir until all ingredients are evenly coated.
Transfer the pasta mixture to a 9x13-inch casserole dish, spreading it evenly. Cover the dish with foil.
Bake in a preheated oven at 350°F (175°C) for 30 minutes.
Carefully remove the casserole from the oven, discard the foil, and sprinkle the remaining mozzarella and Parmesan cheeses over the top.
Return the dish to the oven and bake, uncovered, for an additional 10 minutes or until the cheese is melted and bubbly.
If desired, garnish with chopped basil before serving.