In a saucepan or rice cooker combine rice and 2 cups water. Cook until rice is tender. Remove Skin and bones from Chicken breasts. To make stock, simmer bones in remaining 2 cups water 30 minutes. Strain to remove bones. Remove stems from mushrooms. Cut mushrooms and chicken into thin strips. Add mushrooms, chicken, bamboo shoots, carrots, salt and Msg to stock. Simmer 15 minutes. Gently stir in eggs and onions. Cook over low heat until eggs begin to set. Serve over rice - 6 servings.