Working in batches, if necessary, in a heavy pot over medium-high heat, heat one tablespoon olive oil. Add chicken and cook turning as necessary, until chicken is golden brown. Remove to a plate and tent to keep warm.
Turn heat down to medium-low and add the remaining tablespoon oil. Add annatto, stirring for a minute. Remove the annatto. Add the onion and peppers and cook several minutes until the onion is translucent and the peppers are softening. Add garlic and spices (including the turmeric and paprika if you didn’t use the annatto) and cook, stirring for about a minute.
Return chicken to the pot and stir to coat chicken. Add coconut milk, anywhere from 1 1/2 to 2 cans according to your preference. Simmer about 10 minutes to blend flavors. Taste and adjust seasonings.
Garnish with parsley or cilantro and serve with rice.