For the chicken: Combine the olive oil, vegetable oil, lemon juice, garlic, oregano, salt and pepper. Add the chicken and allow to marinate. Note: The more marinade and the longer it marinates the better, that's what makes the chicken tender and flavorful!
Grill the chicken at about 400 degrees F for 10 minutes each side or until 160 degrees F internal temperature. (Cooking time varies with grill type.) Dice when cool.
For the tzatziki: Combine all the ingredients.
For the balsamic reduction: Combine the vinegar and sugar in a saucepan over medium heat and reduced to half the volume.
For the Greek salsa: Combine all the ingredients.
To assemble each mini chicken souvlaki from the ground up: Layer 1/2-ounce grilled chicken, 1/2 tablespoon tzatziki, 1 drop balsamic reduction and 1 teaspoon Greek salsa on 1 round of pita.