Preheat oven to 400°F and line a baking sheet with parchment paper.
Dice the potato, chicken breast, bell pepper, and onion into uniform half-inch cubes.
In a large mixing bowl, toss the diced ingredients with olive oil, minced rosemary, sea salt, and black pepper.
Spread the mixture evenly across the prepared baking sheet in a single layer.
Roast for 25 minutes, tossing once halfway through, until the potatoes are golden and the chicken is cooked through.
During the last 5 minutes of roasting, cook the egg in a small non-stick skillet until the whites are set.
Transfer the roasted hash to a plate and top with the warm egg before serving.