In a large mixing bowl, combine the mayonnaise, Greek yogurt, curry powder, honey, and lemon juice. Mix until smooth and well combined.
Add the shredded chicken, diced celery, diced apples, raisins or cranberries, and nuts (if using) to the bowl. Stir gently to coat all ingredients with the dressing.
Season with salt and pepper to taste. Adjust the curry powder or honey if you prefer a stronger flavor or more sweetness.
Cover the bowl and refrigerate for at least 30 minutes to allow the flavors to meld.
Serve the curried chicken salad on a bed of lettuce leaves or in a sandwich.