In a large bowl or resealable bag, combine orange juice, lime juice, and olive oil. Add garlic, achiote powder, cumin, coriander, oregano, salt, and pepper. Mix thoroughly to create marinade.

Add chicken to the marinade, ensuring each piece is coated. Marinate for at least 30 minutes at room temperature or up to 4 hours in the refrigerator.

Preheat your grill for indirect heat or bake at 400°F (200°C). Clean and oil the grates if grilling.

Remove chicken from marinade and discard excess. Grill chicken over direct heat for about 20 minutes until charred, then move to indirect heat until internal temperature reaches 165°F.

If baking, place chip on a wire rack in a pan, bake skin-side up for 35-45 minutes until golden brown and reaching an internal temperature of 165°F.

Allow Pollo Asado to rest for 10 minutes before serving. Garnish with lime wedges and chopped cilantro.