To make the tzatziki sauce, combine Greek yogurt, cucumber, garlic, dill, lemon juice, lemon zest and mint in a small bowl; season with salt and pepper, to taste. Drizzle with olive oil. Refrigerate for at least 10 minutes, allowing the flavors to meld; set aside.
Heat 1 tablespoon olive oil in a large skillet over medium high heat. Season chicken with salt and pepper, to taste. Add chicken to the skillet and cook, flipping once, until cooked through, about 3-4 minutes per side. Let cool before dicing into bite-size pieces; set aside.
Preheat oven to 400 degrees F. Place pita onto a baking sheet. Drizzle with remaining 2 tablespoons olive oil; season with salt. Place into oven and bake until golden brown and crisp, about 10-12 minutes.
Top with cucumber, olives, roasted red peppers, onion, feta and tzatziki sauce.
Serve immediately, garnished with dill and parsley, if desired.