Pound the chicken flat, to about ¼ inch thickness.
Place all of the marinade ingredients: garlic, apple cider vinegar, lemon juice, olive oil, greek yogurt, oregano, cumin paprika, salt, pepper, and cayenne pepper, into a bowl and combine.
Pour the marinade into a large ziplock bag. Place the chicken into the bag with the marinade and squish everything around to cover every bit of the chicken. Place this into the fridge for at least 2 hours.
While this is marinating, make the tzatziki sauce. First you want to cut the cucumber lengthwise and remove all of the seeds. Then shred cucumber. Place the cucumber into a kitchen towel and squeeze out any excess liquid. Place this in a medium sized bowl. Add the yogurt, lemon juice, garlic, fresh dill, salt and pepper. Stir it together well. Place this in the fridge and allow the flavors to blend for at least ½ an hour.
When the chicken is finished marinating, remove it from the marinade (discard the marinade) and place it into a large skillet with a tablespoon of oil. Turn the heat to medium and cook the chicken for 3-4 minutes on one side (searing the chicken as it cooks), then flip and continue cooking until fully cooked through.
Place the cooked chicken on a cutting board and allow it to rest for at least 5 minutes before cutting it into strips.
Prepare pita bread (or flatbread) by warming it. Then fill each pita with chicken, optional garnishes, and tzatziki sauce.