Preheat oven to 350°F Line a large baking sheet with foil and spray with cooking spray. Arrange squash, cut side up, on baking sheet. Brush with 3 tablespoons dressing and sprinkle with garlic and pepper. Bake for 30 minutes.
Meanwhile, toss chicken in remaining dressing and marinate while squash is baking. Add chicken to baking sheet and bake 20 minutes. Spread 1/3 cup pasta sauce over chicken and sprinkle evenly with cheese. Bake until cheese is melted an squash is tender, about 10 minutes.
Drag a fork over squash to release the spaghetti-like strands; discard rinds. Serve chicken over squash. Warm remaining sauce and serve on the side.