Preheat the oven to 475°F.
Pat the chicken thighs dry. Season the skin evenly with salt, pepper, garlic powder, dried oregano, and lemon zest.
Heat the oil in a cast-iron skillet over medium-high heat. Place the chicken, skin side down, and cook until fat renders and skin is golden brown, about 8 minutes.
Transfer skillet to oven (chicken should still be skin side down) and bake for 10 minutes. Flip the chicken and continue cooking until skin crisps and meat is cooked through, about 3 minutes more.
Transfer to a plate, then let the chicken rest for about 5 minutes before serving. Serve with lemon wedge to squeeze over the top before serving.