Heat oil in a medium sized kadai or wok.
Add the green curry paste and lemongrass stalks and fry on medium low heat until fragrant, about 1 to 2 minutes. Don’t let the paste burn.
Add half of the coconut milk and fry for about 2 to 3 minutes until oil starts to separate from the mixture.
Add the chicken pieces and fish sauce. Stir to mix.
Add the chicken stock, the remaining coconut milk and sugar.
Turn the heat to medium high and cook for 3 minutes or until the mixture comes to a boil.
Add the vegetables and stir to combine.
Cover and cook for around 8 to 10 minutes until the vegetables are cooked.
Add the green chillies and mix. Check the seasoning and add more sugar or fish sauce if needed.
Turn off the heat and let the curry sit covered for about 10 minutes. This will allow to curry to thicken and become more creamy.
Serve, garnished with chopped coriander leaves.