Heat vegetable oil in a pan over medium heat. Quickly fry green curry paste, lime leaves and chilli if used.
Add coconut milk, fish sauce and sugar.
When the milk starts to gurgle, add the chicken, reduce the heat and cook for about 15 minutes.
Slice the squash into 3x3 cm pieces, add to the chicken and let it cook for another 5 minutes.
Decorate with leaves of basil or mint, or both.