Preheat your oven to 400°F (200°C) and line a large sheet pan with parchment paper for easy cleanup.
Scrub the purple sweet potato thoroughly and dice it into 1/2-inch cubes, then cut the chicken breast into uniform 1-inch pieces.
In a large mixing bowl, toss the sweet potato cubes with half of the olive oil and a pinch of salt until coated.
Spread the sweet potatoes onto the prepared baking sheet and roast for 10 minutes to give them a head start.
While the potatoes roast, use the same bowl to combine the chicken, broccoli florets, minced garlic, remaining olive oil, oregano, salt, and pepper.
Remove the pan from the oven, add the chicken and broccoli mixture, and spread everything out into a single layer so it roasts rather than steams.
Return the pan to the oven and roast for an additional 15 to 18 minutes until the chicken is cooked through and the broccoli has crispy, charred edges.
Remove from the oven and immediately drizzle the entire pan with fresh lemon juice before serving.