In a medium bowl, combine the orange juice, lime juice, olive oil, minced garlic (or garlic paste), achiote powder, ground cumin, ground coriander, dried oregano, sea salt, and black pepper. Whisk everything together until it's well blended.

Place the chicken thighs and/or breasts in a large resealable plastic bag or a glass dish. Pour the marinade over the chicken, ensuring that each piece is well coated. Seal the bag tightly or cover the dish with plastic wrap. Let it marinate in the refrigerator for at least 30 minutes, up to 8 hours.

Preheat your grill to medium-high heat or your oven to 425°F (220°C).

Remove the chicken from its marinade. If grilling, place it directly on the grill grates and cook for about 6-7 minutes per side until you achieve an internal temperature of 165°F (75°C). If roasting, place the chicken on a baking sheet lined with parchment paper and roast for about 35-40 minutes.

Let your chicken rest for about 5-10 minutes before serving to allow the juices to redistribute.

Slice up your pollo asado and serve it with lime wedges and chopped cilantro.