Combine the first 9 ingredients in a large Dutch oven; bring to a boil. Reduce heat, and simmer 15 minutes or until the chicken is done. Remove chicken from pan; cool slightly. Cut into bite-size pieces.
Cook rice sticks in boiling water 5 minutes; drain.
Divide chicken and noodles evenly among 4 large bowls. Ladle 2 cups soup into each bowl. Top each serving with 1/4 cup sprouts and 1 1/2 teaspoons each of onions, cilantro, basil, and mint. Serve with lime wedges; garnish with chopped chile, fish sauce, or chili oil, if desired.