Place chicken breasts in a large glass baking dish or resealable plastic bag.
In a small bowl, whisk together olive oil, lemon juice, za'atar, garlic, salt and pepper then pour marinade over the chicken. Move chicken breasts around to ensure they are evenly coated in mixture. Refrigerate for 30 minutes or up to overnight.
Grill chicken breasts on medium-high heat for 7-8 minutes per side or until internal temperature reaches 155 degrees or higher. Let rest 5-10 minutes before serving to allow juices to re-distribute.