Preheat your oven to 400°F and line a large sheet pan with parchment paper for easy cleanup.
Peel and dice the sweet potato into 1/2-inch cubes, slice the carrots into rounds, and chop the broccoli into bite-sized florets.
Mince the garlic clove and place it in a small bowl with the olive oil, rosemary, thyme, salt, and pepper, whisking to combine.
Place the chicken breast on one side of the sheet pan and arrange the sweet potatoes, carrots, and broccoli on the remaining space.
Drizzle the herb oil mixture over the chicken and vegetables, tossing the produce gently to ensure an even coating.
Roast in the oven for 20-25 minutes, or until the chicken reaches an internal temperature of 165°F and the vegetables are tender and lightly browned.
Let the chicken rest for 5 minutes before slicing to keep it juicy, then serve alongside the roasted vegetables.