To the bowl of a food processor, combine yogurt, mayonnaise, avocado, parsley, dill, tarragon, apple cider vinegar, salt, garlic powder, and black pepper; blend until the mixture is smooth with bright green flecks.
Transfer sauce to a large bowl and add shredded chicken; toss well to combine. Taste and season with a pinch more salt and/or black pepper, if needed. Serve on sandwiches, wraps, with crackers, or over a bed of greens.
