In a large bowl, combine the Greek yogurt, minced garlic, lemon juice, and chopped dill. Stir well to create the tzatziki dressing.
Add the shredded chicken to the bowl, mixing until the chicken is well coated with the dressing.
Fold in the diced cucumber and red onion, ensuring they are evenly distributed throughout the salad.
Season with salt and pepper to taste, adjusting the seasoning as needed.
If desired, gently fold in the crumbled feta cheese for an extra layer of flavor.
Chill the salad in the refrigerator for at least 30 minutes before serving to allow the flavors to meld together.