Preheat oven to 400°F (200°C) and line a large baking sheet with parchment paper for easy cleanup.
Peel and cube the sweet potato into 1-inch pieces and slice the carrot into 1/2-inch thick rounds.
In a large bowl, toss the chicken breast, sweet potato, and carrots with olive oil, minced garlic, rosemary, thyme, salt, and pepper until evenly coated.
Arrange the chicken and vegetables in a single layer on the prepared baking sheet, ensuring they aren't overcrowded to allow for proper browning.
Roast for 25-30 minutes, or until the chicken reaches an internal temperature of 165°F and the root vegetables are fork-tender and caramelized.
Let the chicken rest for 5 minutes before slicing to keep it juicy, then serve alongside the roasted vegetables.