In a large bowl, combine olive oil, white vinegar, minced garlic, paprika, cumin, oregano, salt, black pepper, cayenne pepper (if using), and lime juice. Whisk together until well mixed to create a marinade.
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 ideally overnight for maximum flavor.
Preheat your grill to medium-high heat.
Remove the chicken from the marinade and let any excess drip off. Discard the remaining marinade.
Place the chicken on the grill skin-side down. Grill for about 6-8 minutes, then flip and grill for another 6-8 minutes, or until the internal temperature reaches 165°F.
Once cooked, 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.