In a large bowl, whisk together the olive oil, lime juice, minced garlic, cumin, paprika, oregano, salt, black pepper, and cayenne pepper (if using).
Add the chicken thighs to the marinade, ensuring they are well coated. Cover the bowl with plastic wrap and refrigerate for at least 2 hours, or overnight for best flavor.
Preheat your grill to medium-high heat.
Remove the chicken from the marinade and let any excess drip off. Discard the marinade.
Place the chicken thighs skin-side down on the grill. Cook for about 6-7 minutes, then flip and cook for an additional 6-7 minutes, or until the internal temperature reaches 165°F.
Remove the chicken from the grill and let it rest for 5 minutes before serving.
Garnish with fresh cilantro and serve with lime wedges on the side.