Heat a large pan or wok over medium heat. Add the green curry paste and stir-fry for a minute until fragrant.
Add the chicken pieces to the pan and cook until they are lightly browned on all sides.
Pour in the coconut milk and stir well to combine with the curry paste.
Add the mixed vegetables to the pan and stir them into the curry mixture.
Season the curry with fish sauce and palm sugar. Stir to incorporate the flavors.
Reduce the heat to low and let the curry simmer for about 15 minutes, or until the chicken is cooked through and the vegetables are tender.
Taste the curry and adjust the seasoning if needed.
Remove the pan from the heat and garnish the curry with fresh basil leaves.