Preheat oven to 400°F (200°C) and line a large rimmed baking sheet with parchment paper for easy cleanup.
Scrub the sweet potato clean and slice into 1-inch thick wedges, then cut the chicken breast into similar-sized strips to ensure even cooking.
In a large mixing bowl, combine the sweet potato wedges, chicken strips, and broccoli florets with the olive oil, salt, pepper, garlic powder, and rosemary.
Toss everything thoroughly with your hands or a spatula until every piece is glistening and evenly coated in the herb-oil mixture.
Arrange the mixture on the baking sheet in a single layer, making sure the chicken and potatoes aren't touching too much so they roast rather than steam.
Bake for 22-25 minutes, using tongs to flip the wedges and chicken halfway through, until the chicken is opaque and the potatoes are caramelized and tender.