In a large bowl, whisk together the Greek yogurt, olive oil, lemon juice, garlic, oregano, cumin, paprika, salt, and black pepper.
Add the chicken and turn to coat thoroughly. Cover and marinate in the refrigerator for at least 1 hour, or up to 12 hours.
Preheat a grill to medium-high heat and lightly oil the grates.
Remove the chicken from the marinade, letting any excess drip off. Grill for 5 to 7 minutes per side, or until cooked through and the internal temperature reaches 165°F (74°C).
Transfer to a plate and rest for 5 minutes before serving. Serve warm with your favorite sides.