In a medium bowl, toss chicken strips with the sesame oil and season with salt and pepper, to taste. Heat 3 tbsp vegetable oil over high heat in large frying pan or wok and stir-fry the prepared chicken strips until lightly golden, about 2 to 3 minutes. Add the onion and garlic and stir-fry for 1 to 2 minutes or until onion has softened. Add 2 tbsp more vegetable oil and when hot, stir in the cooked rice and green onions, tossing and mixing thoroughly until very hot. Sprinkle with soy sauce and mix evenly. Remove from heat and stir in chopped cooked egg.