Fry the shallots and garlic in the oil in a medium saucepan for 3–4 minutes until softened. Stir in the curry paste and galangal and cook for 1 minute. Mix in the coconut milk, fish sauce, sugar and lime leaves and bring to the boil.
Stir in the chicken, then cover and simmer for 30 minutes, stirring occasionally until the chicken is cooked through. Stir in the basil leaves, if liked, and serve in bowls with boiled rice.