Preheat your oven to 400°F (200°C) and line a large baking sheet with parchment paper.
Peel and cube the sweet potato and slice the carrots into half-inch rounds.
In a medium bowl, toss the sweet potatoes and carrots with half of the olive oil, half of the salt, and half of the pepper.
Season the chicken breast with the remaining olive oil, salt, pepper, chopped rosemary, thyme, and minced garlic.
Spread the vegetables in a single layer on the prepared baking sheet and roast for 10 minutes.
Move the vegetables to the side, place the chicken breast on the sheet, and roast for an additional 18-22 minutes until the chicken reaches an internal temperature of 165°F.
Remove from the oven and let the chicken rest for 5 minutes before slicing to ensure it stays juicy.
Serve the sliced chicken alongside the tender, caramelized root vegetables.