Combine water and coconut milk in a Dutch oven; bring to a boil over medium heat. Stir in lemongrass, galangal, chiles, and lime leaves; bring to a boil. Add the chicken; cover, reduce heat, and simmer 50 minutes or until chicken is done.
Remove the chicken from broth. Place the chicken in a bowl; chill 15 minutes. Strain broth through a colander into a bowl; discard solids. Return broth to pan.
Remove the chicken from the bones, and cut meat into bite-size pieces. Discard bones. Return chicken to pan. Stir in the fish sauce, and cook for 1 minute over medium heat. Stir in lime juice. Remove from heat. Garnish with cilantro.