Mix lemon juice, olive oil, za’atar, garlic, salt, and pepper together. Put chicken in a zip-locked bag and pour marinade over it. Marinate the chicken at least 2-3 hours or as long as overnight.
For the kabobs:
If using wooden skewers, soak in water at least 30 minutes if grilling outdoors (I usually double them up so they are easier to turn).
Prepare the yogurt sauce by combining the ingredients in a medium bowl. Refrigerate until ready to eat.
Thread chicken onto the skewers. You should have 4 kabobs total.
Preheat the grill over medium heat, oil the grates and cook (indoor or outdoor grill works fine) until the chicken is cooked though, turning often about 12 to 15 minutes.