Preheat your oven to 400°F (200°C) and line a large baking sheet with parchment paper.
Peel and cube the sweet potato into 1/2-inch pieces and slice the carrots into rounds.
In a bowl, toss the sweet potatoes and carrots with half of the olive oil, half of the salt, and half of the pepper.
Mince the garlic and finely chop the fresh rosemary and thyme.
Rub the chicken breast with the remaining olive oil, minced garlic, rosemary, thyme, salt, and pepper.
Place the chicken, sweet potatoes, and carrots on the baking sheet in a single layer and roast for 15 minutes.
Add the broccoli florets to the baking sheet, tossing them quickly in the juices on the pan.
Continue roasting for another 10 to 12 minutes, or until the chicken reaches an internal temperature of 165°F and the vegetables are tender and lightly browned.