Thai Chicken Noodle Soup

Cook the noodles according to package directions. Meanwhile, place the chicken, carrots, celery, onions and ginger in a large pot. Add enough broth to cover (adding water if the broth isn't enough); bring to a boil. Reduce heat, add 1 1/2 tsp salt and 1/2 tsp pepper, and simmer until the chicken is cooked through, 20 to 25 minutes. Transfer the chicken to a bowl and, when cool enough to handle, shred the meat, discarding the skin and bones. Add the coconut milk to the pot and bring to a boil. Stir the chicken, noodles and lime juice into the soup. Sprinkle with the cilantro before serving.