In a large bowl, combine the cooked chicken, cucumber, avocado, cherry tomatoes, red onion, and parsley. Toss gently to mix the ingredients without mashing the avocado.
In a separate small bowl, whisk together the Greek yogurt, lemon juice, olive oil, minced garlic, salt, and pepper until smooth.
Pour the tzatziki dressing over the chicken and vegetable mixture. Gently fold everything together until well coated.
Taste and adjust seasoning with more salt, pepper, or lemon juice if desired.
Serve immediately or chill in the refrigerator for 30 minutes to allow flavors to meld.