Bruise lemongrass and cut into 2.5 cm (1 in) pieces. Cut chicken meat into bite-size pieces. Bring chicken stock and half the coconut milk to the boil, and add chicken, lemongrass, lime leaves, galangal, salt, sugar, and 1 tbsp fish sauce. Simmer for 15 minutes.
Stir in remaining coconut milk. Toss in chillies and add remaining fish sauce and lime juice to taste. Remove from the heat.</