In a bowl, mix olive oil, lemon juice, red wine vinegar, 4 minced garlic cloves, oregano, salt, and pepper. Add chicken thighs and coat evenly. Marinate for at least 1 hour.
Add the peppers and onions back to the pan and stir occasionally until well heated. Adjust seasoning once more and serve immediately with optional parsley as a garnish.
Warm the pita breads, then add slices of chicken, tzatziki sauce, lettuce, slices of tomato, and red onion. Sprinkle on optional feta cheese. Fold and serve.