Preheat your oven to 400°F (200°C) and line a large rimmed baking sheet with parchment paper.
Peel the sweet potato and carrots, then dice the potato into 1-inch cubes and slice the carrots into 1/2-inch rounds.
In a large mixing bowl, toss the diced sweet potatoes and carrots with half of the olive oil, half of the minced garlic, half of the rosemary, half of the thyme, and half of the salt and pepper.
Pat the chicken breast dry with a paper towel, then rub it thoroughly with the remaining olive oil, garlic, rosemary, thyme, salt, and pepper.
Spread the seasoned vegetables in a single layer on the prepared baking sheet and place the chicken breast in the center.
Roast in the oven for 25 to 30 minutes, or until the chicken reaches an internal temperature of 165°F and the root vegetables are tender and golden brown.
Remove from the oven and let the chicken rest for 5 minutes before slicing to ensure it remains juicy, then serve immediately with the roasted vegetables.