Cook the chicken. Bring a large pot of water to a boil. Add the chicken and simmer until fully cooked. Remove the chicken and reserve 1¼ cups of the broth.
Make the curry paste. Pound the dried chilies, galangal, garlic, shallots, and finger root into a smooth paste. Pound the cooked chicken into the curry paste until shredded and well combined.
Cook the curry base. Heat half of the coconut milk in a large pot over medium heat until the oil begins to separate. Stir in the curry paste and chicken mixture, cooking until fragrant.
Finish the soup. Add the remaining coconut milk, reserved chicken broth, fermented fish sauce, fish sauce, sugar, and salt. Bring to a boil, then stir in the kaffir lime leaves and green onions.
Cook the noodles. Boil the vermicelli noodles according to the package directions until just tender. Drain and rinse under cold water.
Assemble and serve. Divide the noodles between serving bowls, ladle the hot soup over the top, and garnish with your favorite herbs, vegetables, lime wedges, fried shallots, fried garlic, or crushed peanuts.