In a large bowl, whisk together the mayonnaise, olive oil, vinegar, honey, celery seed, salt, and pepper.
Add the coleslaw mix, chicken, apple, green onion, and parsley, if using. Toss to coat. Refrigerate or keep cool until ready to eat.
For a delicious flavor boost, sprinkle some pickled jalapeño pepper slices and toasted almond slices on your slaw before eating. Pack separately if taking for lunch.