Preheat the oven to 475°F. Line a large baking sheet with parchment paper and set aside.
In a large bowl, combine the brussels sprouts, baby potatoes, carrots, and onion. Drizzle with olive oil and toss until evenly coated. Spread the vegetables out in an even layer on the prepared baking sheet, making sure they are not crowded so they roast properly.
Pat the chicken thighs dry with paper towels to help the skin crisp. Place the chicken thighs skin side up directly on top of the vegetables, spacing them evenly across the pan.
Brush the chicken thighs with the melted butter, then sprinkle the thyme, salt, and pepper evenly over both the chicken and vegetables.
Roast uncovered for 40 minutes, or until the chicken skin is golden and crisp, the vegetables are tender, and the chicken reaches an internal temperature of 165°F in the thickest part.
Remove the pan from the oven and let the chicken rest for 5 minutes before serving, spooning some of the roasted vegetables and pan juices over the top.