In a large bowl, combine the shredded chicken, celery, red bell pepper, red onion, and parsley. In a separate small bowl, whisk together the olive oil, vinegar, mustard, salt, and pepper until well blended.
Pour the dressing over the chicken mixture and toss everything together until the ingredients are evenly coated. Allow the salad to marinate for at least 30 minutes in the refrigerator before serving to enhance the flavors.
Add fruits such as apples or grapes for a touch of sweetness or include nuts for crunch.
Additionally, if you prefer a creamier texture, you can mix in a dollop of Greek yogurt or mayonnaise to the dressing.