Preheat oven to 400°F (200°C). Line a baking sheet with parchment paper.
In a mixing bowl, toss sweet potatoes with 1 tablespoon olive oil, paprika, and thyme. Spread on half of the baking sheet.
Rub chicken breasts with 1 tablespoon olive oil, garlic powder, black pepper, and lemon juice. Place on the other half of the sheet.
Bake for 20 minutes. Add broccoli to the sheet, tossing lightly with any remaining oil and seasoning.
Continue baking for 12–15 minutes, or until chicken reaches 165°F (74°C) internally and sweet potatoes are tender.
Serve warm, dividing chicken, sweet potatoes, and broccoli among plates.