Preheat a large pot over medium heat. Add the coconut oil. Add the red curry paste and stir fry for 1 minute until aromatic
Add the chicken pieces and stir fry until the chicken turns color, but is not fully cooked yet.
Stir in the coconut milk, water, fish sauce, sugar, lime leaves, and kabocha squash. Bring it to a simmer and then cover and let it cook over low heat (to avoid boiling over) for about 5 minutes
Have a taste and adjust the seasonings as needed. Stir in the basil leaves and turn off the heat