Preheat the oven to 425°F (220°C).
On a baking sheet, combine zucchini, bell pepper, cherry tomatoes, and red onion. Drizzle with olive oil, balsamic vinegar, salt, and black pepper. Toss to coat.
Roast vegetables for 20 minutes, stirring halfway through.
Meanwhile, grill the chicken breasts seasoned with Italian seasoning until fully cooked (about 7-8 minutes per side). Allow to rest, then slice.
Cook pasta according to package instructions. Drain and return to pot.
Add roasted vegetables and sliced chicken to the pasta. Toss with remaining balsamic vinegar if desired.
Serve topped with grated Parmesan cheese.
