In a large mixing bowl, combine the chicken, Greek yoghurt, parsley, dill, garlic, lemon juice, oregano, salt, and pepper. Mix well until the chicken is coated with the marinade. Cover the bowl with plastic wrap and refrigerate for at least 30 minutes or up to 2 hours.

Preheat a large frying pan or skillet over medium-high heat. Remove the chicken from the marinade, letting any excess liquid drip off. Add the chicken to the pan and cook until browned and cooked through, about 5-7 minutes per side. Transfer the chicken to a plate and cover with foil to keep warm.

Warm the pita breads by wrapping them in foil and heating them in the oven at 350°F (180°C) for 5-7 minutes.

In a separate pan, toast the pita breads over medium heat until they're lightly browned and crispy.

In a small bowl, mix together the mixed greens, sliced cucumber, cherry tomatoes, and crumbled feta cheese (if using).

Assemble the pita by placing a few slices of the cooked chicken onto the warmed pita bread, followed by a dollop of tzatziki sauce, and finally a spoonful of the mixed greens and vegetable mixture.

Drizzle with olive oil and serve immediately.