Bring chicken broth to a boil in a medium saucepan. Add carrot and next 3 ingredients; cook, uncovered, 2 minutes.
Break vermicelli into pieces; add vermicelli and chicken to broth mixture. Cook over medium heat 5 minutes, stirring occasionally.
Peel and devein shrimp; chop shrimp. Add shrimp and snow peas to broth mixture. Cook 3 to 5 minutes or until shrimp turns pink. Stir in soy sauce.
To serve, ladle soup into individual bowls, and sprinkle evenly with green onions.