Preheat your oven to 400°F (200°C) and line a large rimmed baking sheet with parchment paper.
Peel and dice the sweet potato into 1/2-inch cubes and slice the carrots into 1/2-inch thick rounds.
In a medium bowl, toss the sweet potato and carrots with 0.5 tablespoons of the olive oil, half of the sea salt, and half of the black pepper.
Spread the vegetables in a single layer on one side of the prepared baking sheet.
Mince the garlic and finely chop the fresh rosemary and thyme.
In a small bowl, combine the remaining olive oil, minced garlic, rosemary, thyme, and the remaining salt and pepper to create a herb paste.
Rub the herb paste evenly over both sides of the chicken breast and place it on the other side of the baking sheet.
Roast in the center of 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 it against the grain to serve with the roasted roots.