Preheat your oven to 400°F (200°C) and line a large rimmed baking sheet with parchment paper for easy cleanup.
Wash and peel the sweet potato and carrots; dice the sweet potato into 1-inch cubes and slice the carrots into 1/2-inch thick rounds.
Mince the garlic clove finely.
In a large mixing bowl, toss the diced sweet potato and carrots with half of the olive oil, half of the rosemary, half of the thyme, and a pinch of salt and pepper.
Pat the chicken breast dry with a paper towel, then rub it with the remaining olive oil, minced garlic, and the rest of the dried herbs, salt, and pepper.
Spread the vegetables in a single layer on the prepared baking sheet, leaving space in the center for the chicken.
Place the chicken breast in the middle of the pan and roast for 20 to 25 minutes, or until the chicken reaches an internal temperature of 165°F and the vegetables are tender and golden.
Remove from the oven and let the chicken rest for 5 minutes before slicing to keep it juicy, then serve immediately with the roasted vegetables.