Preheat your oven to 425°F and line a large sheet pan with parchment paper or lightly grease it.
Pat chicken thighs dry with paper towels. In a small bowl, mix 3 tablespoons olive oil, chopped rosemary, minced garlic, 1 teaspoon salt, and ½ teaspoon pepper.
Rub the rosemary mixture all over the chicken thighs, making sure to get under the skin for maximum flavor.
In a large bowl, toss carrots, Brussels sprouts, and red onion with remaining 2 tablespoons olive oil, balsamic vinegar, ½ teaspoon salt, and ½ teaspoon pepper.
Arrange vegetables around the edges of the sheet pan and place chicken thighs skin-side up in the center, making sure not to overcrowd.
Roast for 28-32 minutes until chicken reaches an internal temperature of 165°F and skin is golden and crispy, and vegetables are tender and caramelized.
Let rest for 5 minutes, garnish with fresh rosemary sprigs, and serve hot with your favorite crusty bread to soak up all those delicious pan juices!