Preheat your oven to 400°F (200°C) and line a large rimmed baking sheet with parchment paper for easy cleanup.
Peel the carrots and sweet potato, then chop them into uniform 1-inch cubes to ensure they cook evenly.
In a large mixing bowl, whisk together the olive oil, minced garlic, dried rosemary, dried thyme, sea salt, and black pepper.
Add the chicken breast and the chopped root vegetables to the bowl, tossing thoroughly until everything is well-coated in the herb oil.
Spread the chicken and vegetables in a single layer on the prepared baking sheet, leaving enough space so they roast rather than steam.
Place the sheet in the oven and roast for 25-30 minutes, or until the chicken reaches an internal temperature of 165°F and the vegetables are tender and lightly browned.
Remove from the oven and let the chicken rest for 5 minutes before slicing to ensure the juices stay locked in.