Preheat your oven to 400°F 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, dried rosemary, dried thyme, sea salt, and black pepper.
Place the sweet potatoes and carrots on the baking sheet and toss them with half of the prepared garlic-herb oil.
Roast the vegetables for 15 minutes to give them a head start on caramelizing.
Rub the chicken breast with the remaining garlic-herb oil until well coated.
Remove the baking sheet from the oven, push the vegetables to the sides, and place the chicken breast in the center.
Return to the oven and roast for an additional 18 to 20 minutes, or until the chicken reaches an internal temperature of 165°F.
Allow the chicken to rest for 5 minutes before slicing and serving with the roasted root vegetables.