Preheat your oven to 400°F (200°C) and line a large baking sheet with parchment paper for easy cleanup.
Dice the sweet potato into half-inch cubes and slice the carrots into uniform rounds to ensure even cooking.
Place the chicken breast, diced sweet potatoes, and sliced carrots onto the prepared baking sheet.
Mince the garlic cloves and whisk them in a small bowl with the olive oil, rosemary, thyme, salt, and pepper.
Drizzle the herb oil over the chicken and vegetables, tossing thoroughly with your hands to ensure every piece is well-coated.
Spread the ingredients into a single layer, making sure the chicken is not covered by the vegetables.
Roast in the center of the oven for 25 to 30 minutes, or until the chicken reaches an internal temperature of 165°F and the vegetables are fork-tender and slightly caramelized.
Let the chicken rest for 5 minutes before slicing to keep it juicy, then serve alongside the roasted roots.