Make the Tzatziki Sauce:
Grate the cucumber and use a clean kitchen towel to squeeze out any excess water.
In a mixing bowl, combine the grated cucumber, Greek yogurt, minced garlic, dill, lemon juice, olive oil, salt, and pepper. Mix well and set aside.
Prepare the Chicken Salad:
In a large bowl, combine the shredded chicken, diced cucumber, red onion, cherry tomatoes, parsley, and feta cheese (if using).
Assemble the Salad:
Pour the prepared tzatziki sauce over the chicken mixture. Toss gently until everything is evenly coated.
Chill and Serve:
Refrigerate the salad for at least 20 minutes to allow the flavors to meld together. Serve cold as a sandwich filling, in a wrap, or over a bed of greens.