Preheat your oven to 400°F (200°C) and line a large sheet pan with parchment paper.
Cut the chicken breast into bite-sized pieces and chop the bell pepper into 1-inch squares.
In a large bowl, toss the chicken, broccoli, and bell pepper with olive oil, lemon juice, oregano, garlic powder, salt, and pepper.
Spread the mixture in a single layer on the prepared sheet pan.
Roast for 15-18 minutes until the chicken is cooked through and the vegetables are tender-crisp.
Remove the pan from the oven and use a spoon to create two small wells in the vegetable and chicken mixture.
Carefully crack one egg into each well.
Return the pan to the oven for 3-5 minutes, or until the egg whites are set but the yolks remain runny.
Serve immediately, drizzling any remaining pan juices over the top.