Preheat your oven to 400°F (200°C) and line a large baking sheet with parchment paper.
Peel and cube the sweet potato into 1-inch pieces and slice the carrots into 1/2-inch rounds.
In a large bowl, toss the sweet potatoes and carrots with half of the olive oil, half of the minced garlic, and a pinch of the salt and pepper.
Spread the vegetables in a single layer on one side of the prepared baking sheet.
Pat the chicken breast dry with a paper towel and rub with the remaining olive oil, garlic, rosemary, thyme, salt, and pepper.
Place the chicken on the other side of the baking sheet.
Roast for 20-25 minutes, or until the chicken reaches an internal temperature of 165°F and the vegetables are tender and caramelized.
Let the chicken rest for 5 minutes before slicing and serving alongside the roasted root vegetables.