Prepare Marinade: To a blender, add cilantro, onion, orange juice, lime juice, garlic cloves, paprika, oregano, kosher salt, cumin, pepper, and ground cayenne pepper (optional). Blend until ingredients are pulverized and combined.
Marinate Chicken: Place chicken in a resealable bag or in a large bowl. Pour marinade atop chicken. If using a storage bag, seal bag, then rotate so the marinade coats chicken. If using a bowl, use tongs to coat chicken in the marinade, then cover bowl with foil or lid. Transfer chicken to refrigerator, and chill for 1-4 hours.
Cook Chicken: Remove chicken from bag or bowl of marinade, letting any excess marinade drip off. Outdoor grill: Preheat outdoor grill to 350 degrees. Rub oil on grates. Grill chicken undisturbed for about 5-10 minutes per side. Grill pan: Preheat a grill pan to medium-high heat. Grill for 3-5 minutes per side. Oven: Preheat oven to 425 degrees F and cook chicken on baking sheet coated in nonstick cooking spray for 18-25 minutes. The chicken is done cooking once it reaches an internal temperature of 165 degrees F on an instant-read thermometer.
Serve: Remove chicken from grill or oven and allow to rest for at least 5 minutes before serving with lime wedges.
