Wash vegetables and meat and cut into bite-sized portions. Pluck Thai basil.
Let the oil get hot in a large saucepan. Add the curry paste and spread with the oil to form a mass. Fry them together briefly. Add the coconut milk. Stir until the coconut milk and paste are mixed. Add the chicken, potatoes and carrots. Add the fish sauce, palm sugar and soy sauce.
Simmer and add the snow peas after about 20 minutes.