Preheat your oven to 400°F (200°C) and line a large rimmed baking sheet with parchment paper for easy cleanup.
Peel the sweet potato and cut it into 1-inch cubes, then cut the chicken breast into similar bite-sized pieces to ensure even cooking.
In a large mixing bowl, combine the chicken, sweet potato cubes, and broccoli florets.
Drizzle the olive oil over the mixture and sprinkle with sea salt, black pepper, garlic powder, dried rosemary, and smoked paprika.
Toss everything thoroughly until the chicken and vegetables are evenly coated in the oil and spices.
Spread the mixture in a single layer on the prepared baking sheet, making sure not to overcrowd the pan so the vegetables roast rather than steam.
Roast in the center of the oven for 20 to 25 minutes, tossing the ingredients halfway through, until the chicken is cooked through and the potatoes are tender and golden.
Remove from the oven and serve immediately while hot and fragrant.