Combine first 3 ingredients in a 2 quart saucepan; bring to a boil. Add chicken; simmer, uncovered, 10 minutes. Add bamboo shoots; simmer 5 minutes. Add vinegar and next 3 ingredients; bring to a boil. Drizzle egg white into soup, sitrring constantly. (Lacy strands will form.) Stir in green onions and snow peas. Combine cornstarch and water; stir into soup mixture. Bring to a boil; boil 1 minute, stirring gently. Serve immediately.