Pat the chicken dry and season all over with ½ teaspoon salt, garlic powder, and black pepper.
In a large non-stick skillet over medium heat, warm 1 tablespoon of olive oil. Add the chicken and cook for about 3-5 minutes or until golden, then flip, cover with a lid, and cook for another 3-5 minutes or until cooked through. Transfer to a cutting board.
Reserve about ¼ cup of the onion for topping. If the skillet looks dry, add in another tablespoon of oil. Add the onion and ¼ teaspoon salt. Cook the onion until it’s softened, about 3-5 minutes, stirring occasionally. Stir in the veggies, remaining ¼ teaspoon salt, and cook for another 3-5 minutes or until the veggies are softened, stirring occasionally.
Meanwhile, chop up the chicken into very small pieces. Add it to the skillet along with the garlic and chilis and cook for 1 minute.
Stir in the soy sauce, lime juice, and butter and cook/simmer for about 2 minutes or until the butter is melted and the liquid has thickened a bit, stirring often.
Make four divots in the veggies and crack the eggs into each one (or you can fry the eggs separately). Cook for about 2 minutes, then cover with a lid and continue to cook until the egg whites are mostly cooked through but the yolks are still runny, about 2 more minutes (they’ll continue to cook as they rest). .
Serve over warm rice, making sure to spoon some of the juices from the skillet over everything. Top with the reserved onion. Break open the yolk and mix the egg into everything.