Preheat oven to 400 degrees Fahrenheit (200 degrees Celsius).
In a large bowl, toss the butternut squash, Brussels sprouts, and sweet potato with 2 tablespoons of olive oil, half the salt, and half the pepper.
Spread the vegetables in a single layer on a parchment-lined baking sheet.
In the same bowl, toss the cubed chicken with the remaining olive oil, rosemary, thyme, minced garlic, and the rest of the salt and pepper.
Place the chicken on a second baking sheet or nestle into the vegetable tray if space permits.
Roast in the preheated oven for 25 to 30 minutes, or until the chicken reaches an internal temperature of 165 degrees Fahrenheit and vegetables are tender.
Remove from oven and let rest for 5 minutes before serving.