Heat the coconut milk in a saucepan until it starts to boil. Add the lemon grass, galangal, chillies, coriander roots, mushrooms and tomatoes and stir for a minute or so.
Add the chicken and stir continuously over a high heat for 8-10 minutes until the chicken is almost done, then season with the fish sauce and lime juice.
Stir over a high heat for another minute or so until the chicken is cooked all the way through. Garnish with coriander leaves and serve immediately.