Boil potatoes for 5 minutes. Add green beans and cook for an additional 3 minutes. They should be tender but not too soft. Drain and set aside.
In a wok, heat some oil and add garlic and chillies. Do not let it brown. Add the curry paste and stir for a few seconds. Pour in coconut milk and let it come to a bubble.
Add fish sauce and balance with sugar. Then add chicken pieces. Turn down the heat to simmer and cook covered for about 8 minutes till the chicken is cooked.
Stir the potatoes and beans in and add lime zest. Finish off by adding the basil. Serve hot with rice.
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