How to Make It
In a small bowl, mix the coconut vinegar with the garlic and chiles. Cover and set aside.
In a large bowl, whisk the coconut vinegar with two-thirds of the grated garlic, the lemongrass, lime juice, brown sugar and ginger. Put each quartered chicken in a large resealable plastic bag. Add the marinade and seal the bags. Refrigerate for 4 to 6 hours.
Meanwhile, in a spice grinder or mortar, crush the annatto seeds to a fine powder. In a small saucepan, melt the butter with the annatto powder over very low heat and cook until fragrant and deep red, 25 to 30 minutes. Remove the saucepan from the heat and stir in 1 teaspoon each of salt and pepper along with the remaining grated garlic.
Preheat the oven to 425°. Heat a grill pan over moderately high heat. Scrape the marinade off the chicken; reserve the marinade. Transfer the chicken to a plate and season with salt and pepper. Grill the chicken in batches over moderately high heat, basting twice with the marinade, until lightly browned on all sides, 10 minutes.
Transfer the chicken to a rimmed baking sheet and baste with the annatto butter. Roast, basting once more with the annatto butter, until an instant-read thermometer inserted into the thickest part registers 165°, about 12 minutes for the breasts and 15 minutes for the legs. Transfer to a platter and serve with steamed rice, lime wedges and the coconut vinegar dipping sauce.
Coconut vinegar is a key ingredient in Filipino cooking. It is available at some Asian markets and from amazon.com. Annatto (achiote) seeds are used to add a distinctive red color to dishes; they are available at most supermarkets.