Preheat the oven to 400°F. Cut 4 pieces of aluminum foil each about 12 inches square.
In a large bowl, combine the chicken, zucchini, bell pepper, green beans, tomato, onions, mushrooms, and garlic. Drizzle the oil, then sprinkle with the rosemary, salt, oregano, and pepper. Toss to combine well.
Divide the mixture evenly among the pieces of foil, arranging it down the center of each piece. Bring up the two sides of the foil and fold over together twice to seal. Fold up the ends tightly.
Place the packets on a rimmed baking sheet and bake for 25 minutes, or until the chicken is cooked through.
Remove the packets, and open the top seams. Sprinkle with grated Parmesan cheese, if using. Eat directly from the packets or transfer to plates.