Cook the penne pasta according to package instructions until al dente, then drain and rinse with cold water.
In a large mixing bowl, combine the diced chicken, cherry tomatoes, diced cucumber, red onion, olives, and parsley.
Add the cooked and cooled pasta into the bowl with the other ingredients.
In a small bowl, whisk together the olive oil, red wine vinegar, dried oregano, salt, and pepper.
Pour the dressing over the salad mixture and toss gently to coat.
Sprinkle feta cheese on top and give a final gentle toss if desired.
Taste and adjust seasoning if necessary before serving.
Chill the salad in the refrigerator for at least 30 minutes before serving.
Serve the salad cold, optionally garnished with additional parsley or feta cheese if desired.