Gyros with Greek Chicken

lbs boneless (, skinless chicken breasts)

extra virgin olive oil (, plus more for brushing)

lemon juice

plain Greek yogurt

red wine vinegar

chopped red onion

garlic

dried oregano

dried thyme

coriander

Salt and freshly ground black pepper (, to taste)

Greek Pita Flatbread (, homemade or store-bought (recipe follows))

Tzatziki sauce (, homemade or store-bought (recipe follows))

Diced Roma tomatoes (, peeled and diced cucumbers, chopped Romaine lettuce, diced red onions, feta cheese, cilantro and Kalamata olives (olives optional))