Preheat your oven to 400°F (200°C) and line a large rimmed baking sheet with parchment paper for easy cleanup.
Peel the sweet potato and carrots, then dice them into uniform 1-inch cubes to ensure even roasting.
In a small bowl, whisk together the olive oil, minced garlic, dried rosemary, dried thyme, sea salt, and black pepper.
Place the chicken breast and the diced vegetables on the prepared baking sheet, then drizzle the garlic-herb oil over everything.
Toss the vegetables and chicken thoroughly with your hands or tongs until every piece is well-coated in the herb mixture.
Spread the ingredients into a single layer, ensuring the chicken has space around it to roast rather than steam.
Bake 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 the juices intact, then serve alongside the roasted roots.