Preheat your oven to 400°F (200°C) and line a large sheet pan with parchment paper for easy cleanup.
Dice the chicken breast, bell peppers, and red onion into uniform 1-inch pieces to ensure even cooking.
Place the chicken and vegetables on the sheet pan and drizzle with olive oil, then sprinkle with sea salt, black pepper, smoked paprika, and dried oregano.
Toss everything together directly on the pan until the chicken and vegetables are well-coated in the oil and spices.
Spread the mixture into a single layer and roast in the oven for 15 minutes, or until the chicken is cooked through and the vegetables are tender.
Remove the pan from the oven and use a spoon to create two small wells in the hash mixture.
Carefully crack one egg into each well and return the pan to the oven for an additional 5 to 7 minutes.
Remove from the oven once the egg whites are fully set but the yolks are still soft and runny.