Preheat oven to 400° F. Spray baking sheet with cooking spray.
Cut squash into cubes, quarter potatoes, peel carrots and cut into 2 inch pieces, and slice Brussels in half. Place all onto baking sheet. Drizzle with olive oil and vinegar. Mince garlic and sprinkle over veggies.
Nestle the chicken into the veggies and then season everything with salt, pepper, oregano, thyme, basil, and rosemary.
Roast for 25-30 minutes, checking to be sure chicken is no longer pink and veggies have become fork tender.