Stir together mayonnaise, sour cream, lemon juice, parsley, chives, tarragon, garlic, salt, and pepper in a bowl until blended.
Using your hands, massage the kale leaves. Combine kale and 3/4 cup of the dressing in a large bowl. Add chicken, celery, carrot, and remaining dressing to bowl; stir until thoroughly combined. Let chicken salad sit at least 30 minutes before serving.