Preheat your oven to 400°F (200°C) and line a large rimmed baking sheet with parchment paper for easy cleanup.
Chop the sweet potato into 1-inch cubes and slice the carrots into half-moons to ensure they cook at the same rate as the chicken.
In a small bowl, whisk together the olive oil, lemon juice, lemon zest, dried rosemary, dried thyme, garlic powder, sea salt, and black pepper to create the marinade.
Place the chicken breast, cubed sweet potatoes, and sliced carrots on the prepared baking sheet in a single layer.
Drizzle the lemon-herb oil over the chicken and vegetables, using your hands or a brush to coat every piece thoroughly for maximum flavor.
Roast in the center of the oven for 25-30 minutes, or until the chicken reaches an internal temperature of 165°F and the vegetables are tender and slightly charred.
Let the chicken rest for 5 minutes before slicing to keep it juicy, then serve immediately alongside the roasted root vegetables.