In a large bowl or resealable bag, combine fresh orange juice, lime juice, olive oil, garlic, achiote powder, ground cumin, ground coriander, dried oregano, sea salt, and black pepper. Mix well until combined.

Add your choice of chicken pieces into the marinade, ensuring each piece is well-coated. Seal the bag or cover with plastic wrap and marinate for 30 minutes at room temperature or refrigerate for up to 4 hours.

Preheat your grill to medium-high heat (375°F-400°F) and ensure to clean and lightly oil the grill grates.

Place the marinated chicken onto the grates skin-side down over direct heat. Cook bone-in pieces for about 20 minutes, flipping every 5 minutes for grill marks.

After grilling, let the chicken rest for 10 minutes covered loosely with foil.

For oven-baked, preheat to 400°F, arrange chicken in a foil-lined baking pan, bake for 35-45 minutes flipping once until internal temperature reads 165°F.