If using day-old rice, fluff it with a fork to break up any clumps. If you don't have day-old rice, spread freshly cooked rice on a baking sheet and let it cool for 10-15 minutes to dry out slightly.
Heat 1 tablespoon of vegetable oil in a large skillet or wok over medium-high heat. Add the chicken pieces and season with salt and pepper. Cook until the chicken is cooked through and golden brown, about 4-5 minutes. Remove from the skillet and set aside.
In the same skillet, add another tablespoon of vegetable oil. Add the chopped onion and cook until softened and translucent, about 3-4 minutes.
Add the minced garlic and cook for an additional 1 minute, or until fragrant.
Stir in the peas, carrots, and red bell pepper, cooking for 2-3 minutes until heated through and slightly softened.
Push the vegetables to one side of the skillet and pour the remaining tablespoon of vegetable oil into the empty side. Add the beaten eggs and scramble until cooked, then mix them with the vegetables.
Add the cooked rice to the skillet, breaking up any large clumps with the back of a spoon.
Stir in the cooked chicken, soy sauce, oyster sauce, and sesame oil. Cook for an additional 2-3 minutes, stirring frequently to ensure the rice is evenly coated with the sauce and heated through.
Taste and adjust the seasoning with salt and pepper, if necessary.
Remove the skillet from the heat and, if desired, stir in the chopped green onions and serve.