Preheat your oven to 400°F and line a large rimmed baking sheet with parchment paper for easy cleanup.
Peel the sweet potato and carrots, then dice the sweet potato into 1-inch cubes and slice the carrots into half-inch rounds to ensure even cooking.
In a large mixing bowl, toss the diced sweet potatoes and carrots with half of the olive oil, half of the salt, and half of the pepper until well coated.
Spread the vegetables in a single layer on one side of the prepared baking sheet and roast for 10 minutes.
While vegetables roast, pat the chicken breast dry and rub with the remaining olive oil, minced garlic, rosemary, thyme, and the rest of the salt and pepper.
Carefully remove the baking sheet from the oven, move the vegetables to one side, and place the seasoned chicken breast on the other side.
Return the sheet to the oven and roast for another 20-25 minutes, or until the chicken reaches an internal temperature of 165°F and the vegetables are tender.
Let the chicken rest for 5 minutes before slicing to keep it juicy, then serve alongside the roasted root vegetables.