Preheat your oven to 400°F and line a large rimmed baking sheet with parchment paper for easy cleanup.
Peel the sweet potato and cut it into one-inch cubes, then slice the carrots into half-inch thick rounds.
Mince the garlic clove finely and place it in a large mixing bowl with the olive oil, rosemary, thyme, sea salt, and black pepper.
Add the cubed sweet potatoes and sliced carrots to the bowl, tossing thoroughly until every piece is well-coated in the herb oil.
Spread the vegetables in a single layer on the prepared baking sheet and roast for 15 minutes to give them a head start.
While the vegetables roast, pat the chicken breast dry and lightly season it with any remaining herb oil from the mixing bowl.
Remove the baking sheet from the oven, push the vegetables to the sides to create space, and place the chicken breast in the center.
Return the pan to the oven and roast for an additional 20 to 25 minutes until the chicken is cooked through and the vegetables are tender.
Allow the chicken to rest for 5 minutes on a cutting board before slicing it against the grain and serving with the roasted vegetables.