Preheat your oven to 400°F (200°C) and line a large baking sheet with parchment paper.
Peel and cube the sweet potato into 1-inch pieces and slice the carrots into rounds.
In a small bowl, whisk together the olive oil, minced garlic, rosemary, thyme, salt, and pepper.
Place the chicken breast, sweet potato cubes, carrots, and broccoli florets on the baking sheet.
Drizzle the garlic-herb oil over the chicken and vegetables, tossing the produce to coat evenly.
Roast for 20-25 minutes, or until the chicken reaches an internal temperature of 165°F and the sweet potatoes are tender.
Let the chicken rest for 5 minutes before slicing and serving alongside the roasted vegetables.