Coat a large grill pan or nonstick skillet with nonstick cooking spray; place over medium heat. Season chicken with salt and pepper to taste. Place chicken in pan; cook 8 to 10 minutes per side or until an instant-read thermometer registers 165°F. Let stand 5 minutes. Thinly slice; set aside.
Meanwhile, in a large bowl combine salad greens, cherries, celery, green onion and pistachios. Drizzle with dressing; toss to coat.
Place salad on 4 plates. Top each salad with sliced chicken, and serve.