Place chicken, yogurt, lemon juice, olive oil, vinegar, salt, pepper, and oregano in bag and let marinate at least 30 minutes, preferably overnight.
Make Tzatziki Sauce
Stir together yogurt, olive oil, lemon juice, vinegar, salt, dill, and garlic. Stir in grated cucumber and taste for seasonings. Squeeze the cucumber to remove excess water before adding to rest of ingredients. Refrigerate for at least one hour and preferably overnight.
Make Greek Salad
Place tomatoes, cucumber, red onion, parsley, olive oil, salt and pepper in bowl. Stir to coat. Season to taste. Refrigerate for at least 30 minutes.
Assembly
Chicken can be cooked on grill or in skillet. To cook on grill -- place chicken on kebobs and heat grill to medium heat. Cook for 5-7 minutes per side or until chicken is full cooked.
To cook chicken on skillet. Heat skillet to medium high heat. Sprinkle with oil. Add chicken and cook for 8-10 minutes, or until chicken is fully cooked and golden brown.
Place chicken in pita bread. You can warm the pita bread to make it pliable. Top with tzatziki sauce and greek salad. Garnish with additional feta and whole parsley leaves, if desired.