In a medium bowl or resealable bag, combine freshly squeezed orange juice, lime juice, olive oil, minced garlic, achiote powder, ground cumin, ground coriander, dried oregano, sea salt, and ground black pepper. Whisk or shake until well blended.

Add 3 pounds of your chosen chicken to the marinade, ensuring each piece is thoroughly coated. Allow the chicken to marinate for 30 minutes at room temperature or up to 4 hours in the refrigerator.

Preheat your grill to medium-high heat (about 375°F to 450°F) with direct and indirect cooking zones.

Remove the chicken from the marinade and place it skin side down on the grill grates. Grill for approximately 20 minutes, turning occasionally.

Transfer the chicken to the indirect heat side of the grill. Close the lid and continue cooking for another 15-20 minutes, until the internal temperature reaches 160°F-165°F.

Once cooked, remove the chicken from the grill and let it rest under foil for about 10 minutes before serving.