Preheat your oven to 400°F (200°C) and line a large rimmed baking sheet with parchment paper.
Dice the chicken breast into 1-inch cubes and chop the bell pepper and broccoli into bite-sized pieces.
Place the chicken cubes, chickpeas, broccoli florets, and bell pepper onto the prepared baking sheet.
Drizzle the olive oil over the mixture and sprinkle with sea salt, black pepper, garlic powder, and smoked paprika.
Toss the ingredients thoroughly with your hands or a spatula until everything is evenly coated in oil and spices, then spread into a single layer.
Roast in the center of the oven for 20 to 25 minutes, or until the chicken is cooked through and the vegetables are tender with lightly charred edges.
While the medley roasts, whisk together the Greek yogurt, lemon juice, and dried oregano in a small bowl until smooth.
Remove the tray from the oven, transfer the roasted medley to a serving bowl, and drizzle the zesty yogurt sauce over the top before serving warm.