Heat sesame oil in a large skillet over medium heat. Add onion and sauté until soft. Add cooked chicken and 2 tablespoons soy sauce; stir-fry for 5 to 6 minutes.
Stir in carrots, celery, red bell pepper, pea pods, and green bell pepper; stir-fry for 5 minutes. Mix in cooked rice until thoroughly combined.
Stir in scrambled eggs and 1/3 cup soy sauce; cook until heated through and serve hot.