Mix all ingredients in a shallow glass dish or bowl. Cover and refrigerate to marinate for 4 hours.
Assemble the chicken hearts on metal skewers, or bamboo skewers that have soaked in water for 10 to 15 minutes.
Barbecue the skewers for 15 minutes, or until no longer pink in the centre, turning halfway through.
Also called achiote powder, it can be found at Asian or Latin American shops and markets, or online. Annatto is mostly used for the vibrant colour it imparts, so in a pinch you could either omit it from the recipe or use equal parts paprika and turmeric instead.