In a medium bowl, combine fresh lime juice, orange juice, olive oil, and minced garlic. Whisk in smoked paprika, ground cumin, chili powder, dried oregano, salt, and pepper until well-blended.

Place the chicken thighs or breasts into a large resealable plastic bag or a shallow dish. Pour the citrus marinade over the chicken, ensuring it is thoroughly coated. Seal the bag or cover the dish and refrigerate for at least 2 hours, ideally overnight.

Preheat your grill to medium-high heat, about 375°F-400°F.

Remove the chicken from the marinade, allowing any excess to drip off, then place it directly onto the hot grill. Grill for approximately 5-7 minutes per side, or until the internal temperature reaches 165°F.

Once cooked, carefully remove the chicken from the grill and let it rest for about 5 minutes.

Transfer the rested chicken to a serving platter and garnish with chopped cilantro and lime wedges.