In a small bowl combine Greek yogurt, garlic, cumin, sugar, cucumber, and salt and pepper. Stir and refrigerate until ready to use.
Pound chicken as thin as you can get it. Even if you have purchased the thin sliced chicken you still want to get it as thin as possible. Place chicken in a bowl and combine with vinegar, oregano, paprika, and salt and pepper. Cover and refrigerate for at least 30 minutes.
In the mean time, peel you potato and cut into 1/4 inch strips. Place cut potato in cold water for at least 15 minutes. Blanching the potatoes before frying will ensure a crispier fry.
In a large skillet heat vegetable oil. Personally, I regulate the temperature by instinct. I let the oil heat up and test it with a drop of water; if the water shoots back I know the oil is hot enough. If you aren't comfortable with this method you want the oil to stay around 360 degrees. When the oil is hot enough drop fries inches Depending on the thickness of your fry and your temperature control your fries will take anywhere from 10-20 minutes. You want your fries to have a deep golden brown. Keep a careful eye on them and flip if necessary.
Heat a medium DRY skillet. No oil is necessary to sauté the chicken. Begin to sauté chicken. It should only take about 1 minute on each side depending upon how thinly you pounded it. Let chicken rest under tin foil until you are ready to assemble.
You can either toast your pita or microwave it. I prefer to microwave it so it is more pliable (only about 20 seconds). Place 2 heaping tablespoons of the tzatziki sauce and spread over pita. Then place half of the chicken, place mostly in the center, making sure that you are able to fold in the sides. Traditionally, fries are to be placed on top of chicken WITHOUT drying off the oil; however this is entirely up to you. Place fries on top of chicken and top with tomatoes, lettuce, and red onions. Serve with extra tzatziki sauce on the side for dipping.