In a large mixing bowl, combine olive oil, lemon juice, red wine vinegar, paprika, oregano, salt, pepper, and minced garlic.
Add the chicken breasts and coat thoroughly with the marinade.
Cover and refrigerate for at least 1 hour. For maximum flavor, marinate for up to 8 hours.
Heat a large skillet over medium-high heat.
Add the marinated chicken and any remaining marinade to the skillet.
Cook for 4–5 minutes per side, or until the chicken reaches an internal temperature of 165°F (74°C).
Remove the chicken from the skillet and allow it to rest for a few minutes.
Slice the chicken into thin strips.
Return the sliced chicken to the skillet for 1–2 minutes to absorb any remaining juices and marinade.
Warm the pita breads if desired.
Assemble the Greek Chicken Pita Wraps by layering lettuce or cabbage, cucumber, tomatoes, and red onion onto each pita.
Add the sliced chicken.
Top with tzatziki sauce and crumbled feta cheese.
Fold or wrap the pita and serve immediately.