Beat egg and water together in small bowl. Melt butter in a large skillet or wok over medium-low heat; add egg and cook without stirring, 1 to 2 minutes. Remove egg from skillet and cut into shreds; set aside.
Heat oil in the same skillet. Add onion; cook and stir until soft, about 3 minutes. Stir in rice, chicken, soy sauce, and pepper. Cook and stir for about 5 minutes; stir in shredded egg. Serve hot.
