Grill or pan-cook the chicken breasts for about 10 minutes, or until fully cooked (internal temperature should reach 165°F). Let them rest for 5 minutes before shredding or chopping into bite-sized pieces.
While the chicken is cooking, chop the celery, onion, and apple (if using). Set them aside in a large mixing bowl along with the mixed greens.
In a small bowl, whisk together the plum preserves, Dijon mustard, apple cider vinegar, and mayonnaise until smooth. Season with salt and pepper to taste.
Add the cooked chicken to the mixing bowl with the veggies. Pour the dressing over the salad and toss everything together until well-coated.
For the best flavor, let the salad chill in the fridge for 30 minutes before serving.
Garnish with chopped nuts if desired, and enjoy the salad on its own or served with a side of crusty bread.