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 until no longer pink in the center, about 5–7 minutes depending on size.
Add the minced garlic to the skillet with the cooked chicken and sauté for about 1 minute, until fragrant.
Stir the pasta sauce, cooked chicken with garlic, and chopped basil into the drained ziti until evenly coated.
Spread half of the pasta mixture into the prepared baking dish. Sprinkle with 1/2 cup grated Parmesan and 1 cup shredded mozzarella. Top with the remaining pasta mixture.
Cover the dish with aluminum foil and bake for 20 minutes.
Uncover, sprinkle the remaining 1/2 cup Parmesan and 1 cup mozzarella over the top, and bake uncovered for an additional 8 minutes until cheese is melted.
Let the baked ziti rest a few minutes, then top with additional chopped basil if desired before serving.
