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 skillet over medium heat. Add the chicken and cook until no longer pink in the center, about 5–7 minutes depending on piece size.
Add the minced garlic to the skillet with the cooked chicken and cook 1 minute more, until fragrant.
Stir the pasta sauce, cooked chicken with garlic, and chopped basil into the drained ziti until evenly coated.
Pour half of the pasta mixture into the prepared baking dish, then 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.
Remove the foil, sprinkle the top with the remaining 1/2 cup Parmesan and 1 cup mozzarella, and bake uncovered for an additional 8 minutes, until cheese is melted.
Optionally top with additional chopped basil before serving.