Preheat your oven to 400°F and line a large baking sheet with parchment paper for easy cleanup.
Peel and chop the carrots and sweet potato into uniform 1-inch pieces to ensure they roast evenly.
In a medium bowl, toss the chopped vegetables with 0.5 tbsp of the olive oil, 1 minced garlic clove, and a pinch of salt and pepper.
Spread the vegetables in a single layer on the prepared baking sheet and roast for 10 minutes.
While the vegetables roast, pat the chicken breast dry and rub it with the remaining 0.5 tbsp of olive oil, 1 minced garlic clove, rosemary, thyme, salt, and pepper.
Remove the baking sheet from the oven, move the vegetables to the edges, and place the seasoned chicken breast in the center.
Return the pan to the oven and roast for an additional 20-25 minutes, or until the chicken reaches an internal temperature of 165°F.
Allow the chicken to rest for 5 minutes before slicing to lock in the juices, then serve alongside the golden roasted vegetables.