Preheat your oven to 400°F (200°C) and line a large sheet pan with parchment paper for easy cleanup.
Cut the chicken breast into uniform 1-inch cubes and place them in a large bowl along with the broccoli florets.
In a small ramekin, whisk together the olive oil, lemon juice, lemon zest, minced garlic, oregano, salt, and pepper until emulsified.
Drizzle the lemon-herb mixture over the chicken and broccoli, tossing well to ensure every piece is evenly coated in the marinade.
Spread the chicken and broccoli 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 oven for 18 to 20 minutes, or until the chicken is cooked through and the broccoli is tender with slightly charred, crispy edges.
Serve the roasted chicken and broccoli over the warm cooked quinoa, drizzling any remaining juices from the pan over the top.