In a large pot, combine the coconut milk and chicken broth and bring to a gentle simmer over medium heat.
Add the lemongrass, kaffir lime leaves, and galangal to the pot. Simmer for about 5 minutes to infuse the flavors.
Add the chicken slices and mushrooms (and bell pepper if using) to the pot. Cook until the chicken is cooked through, about 10 minutes.
Stir in the fish sauce, sugar, and sliced Thai chilies. Continue to simmer for another 5 minutes.
Remove the pot from heat and discard the lemongrass, kaffir lime leaves, and galangal pieces.
Stir in the lime juice and adjust the seasoning as needed.
Serve the soup hot, garnished with chopped cilantro and Thai basil leaves if desired.