Prepare an outdoor grill for medium heat.
Whisk the oil, oregano, lemon zest and juice and garlic in a large bowl. Add the chicken, toss to coat and set aside for 10 minutes at room temperature.
Remove the chicken from the marinade and pat dry and sprinkle generously with salt and pepper.
Lightly oil the grill grates and grill the chicken, skin-side down, until lightly charred, 2 to 4 minutes. Flip and cook for an additional 5 minutes. Cover the grill and cook until no longer pink near the bone and an instant-read thermometer inserted into the deepest part of each chicken thigh reads 165 degrees F, about 5 more minutes. Transfer to a platter and rest for at least 5 minutes before serving. Serve with a green salad.
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