Set a medium-size nonstick skillet over medium-high heat. Spray with olive oil, and brown the chicken 2 minutes on each side. Season each cooked side with salt and pepper. Add the pasta sauce and let simmer for 4 minutes. Sprinkle with Parmesan cheese, cover with a lid, and let sit 1 minute. Divide between 4 plates and serve with the pasta and broccoli.
Bring a large pot of water to a boil and add the pasta. Cook 5 minutes, add broccoli, and continue to cook 4 minutes. Drain and toss with olive oil; season with salt and pepper.