Preheat your oven to 400°F (200°C). Peel and dice the sweet potato into small cubes, and place them on a baking sheet. Drizzle half of the olive oil, sprinkle a pinch of salt and pepper, and toss to coat evenly.
Roast the sweet potatoes in the oven for about 20-25 minutes or until tender and lightly crisp, stirring halfway through.
While the sweet potatoes roast, dice the chicken breast into small bite-sized pieces. In a bowl, lightly season the chicken with salt and pepper.
Heat a non-stick skillet over medium-high heat and add the remaining olive oil. Once hot, add the chicken pieces and saut é until they are golden brown and crispy, approximately 5-7 minutes. Transfer the chicken to a plate.
In the same skillet, add the diced onion and red bell pepper. Sauté until softened, about 3-4 minutes.
Return the crispy chicken to the skillet with the vegetables and stir together.
Make a small well in the center of the hash and crack the egg into it. Allow the egg to cook to your desired doneness (sunny side up or over easy) by covering the pan for 2-3 minutes.
Once the egg reaches your preferred state, gently mix the yolk with the hash if desired, then serve the savory hash alongside the roasted sweet potatoes.