Preheat oven to 400°F (200°C).
Peel and chop the sweet potato and carrots into 1-inch cubes.
Mince the garlic cloves and finely chop the fresh rosemary and thyme.
In a large bowl, whisk together the olive oil, minced garlic, rosemary, thyme, salt, and pepper.
Add the chicken breast and chopped vegetables to the bowl, tossing thoroughly to ensure everything is evenly coated in the herb oil.
Arrange the chicken and vegetables in a single layer on a parchment-lined baking sheet.
Roast for 25-30 minutes, or until the chicken reaches an internal temperature of 165°F and the vegetables are tender and browned.
Let the chicken rest for 5 minutes before slicing and serving alongside the roasted roots.