Prep the cucumber by dicing it, then gently press between paper towels to remove excess moisture.
In a large mixing bowl, whisk together the Greek yogurt, lemon juice, minced garlic, chopped fresh dill, salt, and black pepper to create the dressing.
Fold the shredded chicken, prepared cucumber, and diced red onion into the yogurt mixture until all ingredients are evenly coated.
Cover the bowl and refrigerate for at least 30 minutes to allow the flavors to blend before serving.