Preheat the oven to 425 degrees Fahrenheit and line a large baking sheet with parchment paper.
Place the butternut squash, Brussels sprouts, carrots, and red onion in a large bowl. Add the olive oil, thyme, salt, and black pepper. Toss until the vegetables are evenly coated.
Spread the vegetables in a single layer on the prepared baking sheet. Nestle the chicken thighs among the vegetables, skin side up.
Roast for 35 to 40 minutes until the chicken reaches an internal temperature of 165 degrees Fahrenheit and the vegetables are tender with some browned edges.
Remove the pan from the oven and let it rest for 5 minutes. Sprinkle the chopped parsley over the top before serving.