In a large skillet or wok, stir-fry chicken in 2 tablespoons oil until no longer pink, 6-8 minutes. Remove chicken and set aside. , In the same skillet, stir-fry carrots in remaining oil for 2 minutes. Add onion; stir-fry until vegetables are tender, 2-4 minutes longer. , Combine soy sauce and brown sugar; add to skillet. Bring to a boil. Return chicken to skillet. Boil until sauce is slightly thickened, about 5 minutes. Serve with rice. Sprinkle with sesame seeds and green onions if desired.