Preheat your oven to 400°F and line a large sheet pan with parchment paper for easy cleanup.
Peel the sweet potato and cut it into 1/2-inch cubes, then place them on one side of the prepared baking sheet.
Drizzle the sweet potatoes with half of the olive oil and a pinch of salt and pepper, tossing to coat evenly.
In a small ramekin, mince the garlic and combine it with the remaining olive oil, rosemary, thyme, salt, and pepper.
Place the chicken breast on the other side of the pan and rub the garlic-herb oil mixture over both sides of the meat.
Roast the chicken and sweet potatoes for 15 minutes.
Remove the pan briefly to add the broccoli florets to the center, tossing them in any residual oil on the pan.
Return the pan to the oven for another 10 to 12 minutes, or until the chicken reaches an internal temperature of 165°F.
Remove from the oven and finish the chicken and broccoli with a bright squeeze of fresh lemon juice before serving.