Combine everything but the chicken in a large ziplock bag (I prefer to zip it closed and just mash it all together). Add the chicken to the bag and mix with the marinade until everything is completely covered. Seal the bag and let marinate in the refrigerator for at least 3-4 hours.
Remove chicken from the marinade and cook, either grilling or in a frying pan, about 3-4 minutes on each side, depending on the thickness of your chicken. Serve in the pita breads, with tzatziki and the veggies of your choice.
Combine all ingredients in a small bowl. Cover and chill for at least 30 minutes before using, but it gets better after at least a couple of hours.