In 3 1/2 or 4-quart slow cooker, layer chicken thighs, carrots, celery, bamboo shoots, water chestnuts and contents of seasoning packet from soup mix. Pour broth over top.
Cover; cook on Low setting for 7 to 8 hours.
About 10 minutes before serving, remove chicken from slow cooker; place on large plate. Shred chicken with 2 forks; return to slow cooker and mix well. Coarsely break noodles from soup mix into soup. Stir in thawed sugar snap peas. Cover; cook an additional 10 minutes or until noodles are tender.
Just before serving, stir in onions. If desired, add salt and pepper to taste.