Bring the broth and water to a boil in a large saucepan. Add the bouillon powder, onion, carrots, celery, and bay leaf. Cover the pan with a lid and boil on medium heat until the vegetables are tender, about 15 minutes.
Add the corn, chicken, salt, and pepper; return to a boil for 2 minutes. Add the noodles to the soup; cook at a medium boil until the noodles are al dente, about 7 minutes. Remove the pan from heat and keep covered until ready to serve. Noodles will continue to soften in the warm broth. Remove the bay leaf before serving.