In a medium-size bowl, add in the olive oil, lemon juice, za'atar, garlic, salt, and black pepper. Whisk together to combine. Set aside.
Trim off any excess fat and skin from the chicken thighs. Add the chicken to the bowl with the dressing.
Using tongs or your hands, turn the chicken to coat evenly with the dressing. Set aside to marinate and allow the poultry to come closer to room temperature; 20-30 minutes (if using a charcoal grill, start the preheating process immediately after this).
Preheat the grill to 425 degrees.
Place the chicken on the grill with skin side up. Cover, grill for 5 minutes, and flip the chicken. Cover, grill for another 5 minutes, and flip again.
Repeat this process until the chicken is cooked through, about 25 minutes.
Remove from heat and let rest a few minutes before serving with lemon wedges.