Preheat the oven to 350°F (175°C) and spray a 9x13-inch baking dish with cooking spray.
Bring a large pot of salted water to a boil and cook the ziti until al dente according to package directions; drain well and return to the pot.
Season the bite-size chicken pieces generously with salt and pepper.
Heat 1 tablespoon olive oil in a medium skillet over medium heat. Add the chicken and cook, stirring occasionally, until no longer pink in the center.
Add the minced garlic to the skillet with the cooked chicken and cook about 1 minute until fragrant.
Stir the pasta sauce and chopped basil into the cooked ziti, then fold in the cooked chicken so everything is evenly coated.
Pour half of the pasta mixture into the prepared baking dish, sprinkle with 1/2 cup grated Parmesan and 1 cup shredded mozzarella, then top with the remaining pasta.
Cover the dish with aluminum foil and bake for 20 minutes.
Remove the foil, sprinkle the remaining 1/2 cup Parmesan and 1 cup mozzarella on top, and bake uncovered for 8 minutes until cheese is melted.
Remove from the oven and, if desired, top with additional chopped basil before serving.