In a mixing bowl, whisk together olive oil, lemon juice, Greek yogurt, red wine vinegar, chopped red onion, garlic, oregano, thyme, coriander and season with salt and freshly ground black pepper to taste. Place chicken in a gallon ziploc bag, pour marinade over chicken, seal bag while pressing out excess air and transfer to refrigerator to marinate 2 – 4 hours. Remove chicken during the last 30 minutes of marinating to rest at room temperature before grilling (leave in marinade). Brush grill grates lightly with oil and preheat grill over moderately high heat. Once hot, add chicken and grill until cooked through (internal temperature should register 165 degrees on an instant read thermometer), rotating once halfway through cooking. Remove from grill transfer to plate and brush chicken lightly with olive oil then cover with foil and allow to rest 10 minutes. Dice into strips.
To assemble gyros: layer chicken in a row along center of pita, top with lettuce, tomatoes, cucumbers, Kalamata olives, red onion, feta, cilantro and tzatziki sauce. Wrap and serve.