In a large bowl, combine the chicken thighs, za'atar, olive oil, and a pinch of salt. Mix well, ensuring that the chicken is well-coated with the za'atar and olive oil mixture.
Let it marinate for at least 30 minutes to an hour. For best results, marinate for up to 4 hours or overnight in the refrigerator.
Once marinated, thread the chicken pieces onto the skewers.
Preheat a grill or grill pan over medium-high heat, then place the skewers on the grill. Cook for 5-7 minutes on each side, or until the chicken is fully cooked and has a nice char.
Once cooked, remove the chicken skewers from the heat and let them rest for a few minutes before serving.
Meanwhile, in a medium bowl, combine the Greek yogurt, lemon juice, and grated garlic. Mix well and season with salt to taste.
Transfer chicken to a large plate and serve with yogurt sauce.