Bring coconut milk and chicken stock to a boil in a pot over high heat. Reduce heat to medium. Add cilantro, lemongrass, galangal, Thai chile peppers, and kaffir lime leaves; simmer for 5 minutes.
Increase heat to medium-high heat. Add chicken; simmer until no longer pink in the center, about 7 minutes. Stir in cabbage; cook until wilted, about 3 minutes. Remove soup from heat; stir in lime juice and fish sauce.