Using the same skillet, heat the vegetable oil over medium heat. Add the chopped onion and sauté for about 3 minutes until it becomes soft and translucent. Stir in the cold, cooked rice, ensuring it is well separated. Add the chopped chicken, soy sauce, and ground black pepper, and continue to cook, stirring frequently, for around 5 minutes. Finally, mix in the shredded egg and stir until everything is well combined and heated through. Serve immediately while hot.