Preheat your oven to 400°F (200°C) and line a large rimmed baking sheet with parchment paper.
Peel the sweet potato and dice into 1-inch cubes; slice the carrots into 1/2-inch thick rounds.
Mince the garlic cloves and finely chop the fresh rosemary and thyme leaves.
In a large mixing bowl, toss the sweet potatoes and carrots with half of the olive oil, half of the garlic, and a pinch of salt and pepper.
Place the chicken breast on the prepared baking sheet and rub with the remaining olive oil, garlic, rosemary, thyme, salt, and pepper.
Arrange the vegetables in a single layer around the chicken on the baking sheet to ensure even roasting.
Roast for 25 to 30 minutes, or until the chicken reaches an internal temperature of 165°F and the vegetables are fork-tender and slightly browned.
Remove from the oven and let the chicken rest for 5 minutes before slicing to keep it juicy.