In a zip top bag, add all of the ingredients for the chicken. Shake the bag so the chicken is coated and place it in the refrigerator to marinate for at least 3 hours.
Meanwhile, make the tzatziki. Mix all of the ingredients for the tzatziki in a bowl, cover with plastic wrap and place in the refrigerator for the flavors to come together while the chicken marinates.
Heat a cast iron pan over medium high heat. Add the chicken to the pan along with the marinade. Cook the chicken until golden brown and cooked through; about 5 minutes on each side. Remove to a cutting board and let the chicken rest for 5-10 minutes. Slice the chicken into strips and add it back to the pan over medium heat to crisp up around the edges; about 3 minutes. At this point, you can taste the chicken and add additional salt, cumin or Greek seasoning to your taste.
Serve the chicken with the tzatziki, vegetables and warm pita.