Pound each piece of chicken to an even thickness of 1/4- to 1/2-inch thick. I do this by placing each chicken breast one-by-one in a freezer ziploc bag (since the plastic is thicker than a regular storage bag), leaving the bag open to let air out, and pounding with the smooth end of my meat mallet or the bottom of a heavy skillet.
ALTERNATE METHOD: If the chicken breasts you are using are really thick, you can cut them in half (like a hamburger bun) to form two thinner cutlets.
Whisk together all the marinade ingredients: parsley, lemon juice, red wine vinegar, sesame oil, olive oil, garlic cloves, marjoram, thyme, oregano, salt and pepper.
Place the chicken in a baking dish or ziploc bag and pour the marinade over the top. Turn to coat the chicken in the marinade. Refrigerate for at least 30 minutes and up to 2 hours (any longer and the acidity in the marinade can "cook" the chicken and turn it white).
Preheat a grill to medium. Grill the chicken until cooked through and an instant-read thermometer reads 165 degrees F, about 3-4 minutes per side, depending on the thickness of the chicken.
Let the chicken rest, covered, for 5-10 minutes before slicing into strips and serving.
Notes
Spices: this chicken is an adaptation from a za'atar chicken recipe (which is a Mediterranean spice blend made up of sesame, thyme, marjoram and sumac). If you don't have marjoram in your spice cabinet, you can try using another dried herb (maybe basil or a little more thyme and oregano?). Obviously it will change the flavor just a bit but since this isn't necessarily a 100% authentic za'atar recipe, I think it will be just fine (although it is delicious with the marjoram).