Prepare Chicken Gyro Marinade by combining extra virgin olive oil, lemon juice, red wine vinegar, minced garlic, Greek oregano, paprika, ground cumin, salt and pepper into a small mason jar and shaking vigorously. Set aside.
Cut chicken breast into small, evenly sized cubes.
Place cut up chicken breast in a zip lock bag and pour Chicken Gyro Marinade into bag. Coat all chicken pieces well with the marinade and place in the refrigerator for 1 hour or more.
Place 6 wooden skewers into water to soak.
Remove marinated chicken from refrigerator and thread 3-4 pieces of chicken on each skewer.
Grill chicken skewers for 10-12 minutes, or until done, turning once in between.
Brush pita bread with extra virgin olive oil and place on grill for 2-3 minutes, or until done, turning once in between and careful not to burn pita bread.
Serve chicken and pita bread with Tzatziki Sauce, sliced tomatoes, and sliced red onions.