Cut the bottom 6 inches of lemongrass into 1 inch pieces and crush with the sides of a cleaver. In a large pot, bring the broth, lemongrass, and ginger to a boil. Reduce the heat to medium, add the coconut milk and the fish sauce, cover, and simmer for 8 minutes. Add the chicken, mushrooms, lime juice, and chili and cook until the chicken turns opaque, about 5 minutes. Add the basil leaves just before serving. Ladle into individual bowls.
