Combine marinade ingredients into a bowl or resealable bag and mix thoroughly.
Trim any excess skin from your chicken quarters (save it for rendering later). Then make some shallow slits in the chicken to help the marinade penetrate into the meat. Add the chicken to the marinade to coat evenly. Cover and place in the refrigerator for 6–8 hours, flipping once halfway through.
While chicken is marinating, place the trimmed chicken skin into a saute pan over medium heat. Render the fat out of the skin, then remove the skin from the pan.
Add the margarine, annatto seeds, crushed garlic cloves, and a pinch of salt to the rendered chicken fat. Let it gently bubble for a few minutes to infuse color and flavor, then strain out the solids. Keep warm for basting.
Set up your grill for two-zone cooking, establishing a medium high heat directly over the coals or active gas burner. While the grill is preheating, remove the chicken from the marinade and pat it dry with paper towels.
Place the chicken on the grill over direct heat and flip often. Once the chicken starts to take on some color, start brushing on the basting oil and continue cooking, flipping and basting every few minutes till desired char is created. Then, place the chicken skin side up over indirect heat. Baste one more time and close the lid, allowing the chicken to finish cooking. Remove the chicken when it reaches 185°F internal, usually about 30–35 minutes total
Brush the chicken one last time with warm basting oil and serve it up with rice, a squeeze of lime, and any extra oil on the side for dipping.