In a large non-reactive bowl, combine all the ingredients under chicken marinade. Add chicken and toss to coat. Season generously with salt and pepper. Cover and let marinate for 2 hours or overnight.
Prepare tzatziki sauce an hour or two before eating — you can also make it the day before. If the liquid separates, just drain it off and stir it. Combine all ingredients in a small bowl and season with salt and pepper. Make sure you really squeeze as much water out of the cucumber as you can!
Thread equal amounts of chicken on each skewer. Heat your grill or grill pan to medium heat. Spray with nonstick Pam and grill on each side for about 4-5 minutes, turning 3 times, or until done. Make sure to watch the chicken as all grills will be different.
Remove from grill and cover with foil. Let rest for 10 minutes.
Cut chicken into smaller pieces, I halved each piece after pulling it off the skewer.
Heat your pita breads over the stove or grill until pliable.
Fill with tomatoes, lettuce, onion, feta and chicken. Serve with tzatziki sauce.