Preheat your oven to 400°F (200°C) and line a large baking sheet with parchment paper.
Peel the sweet potato and cut into 1/2-inch cubes; slice the carrots into 1/4-inch thick rounds.
In a mixing bowl, toss the sweet potatoes and carrots with half of the olive oil, half of the rosemary, thyme, salt, and pepper.
Spread the vegetables in a single layer on one side of the prepared baking sheet.
Mince the garlic and combine it with the remaining olive oil and herbs in a small bowl.
Rub the herb-garlic mixture all over the chicken breast and place it on the other side of the baking sheet.
Roast in the oven for 20 to 25 minutes, or until the chicken reaches an internal temperature of 165°F and the vegetables are fork-tender.
Remove from the oven and let the chicken rest for 5 minutes before slicing to keep it juicy.