In a bowl, combine chicken and teriyaki sauce; marinate for at least 2 hours to overnight. Drain the chicken from the marinade.
Preheat grill or grill pan to medium heat.
Add chicken to grill or grill pan, and cook, turning occasionally, until chicken is completely cooked through, reaching an internal temperature of 155 degrees F, about 5 - 6 minutes per side. Allow chicken to rest for 3 - 4 minutes and cut into strips
To assemble the salad, place romaine lettuce in a bowl; top with chicken, cabbage, carrots, chow mein noodles, mandarin oranges, cashews, cilantro and green onions. Dress and serve.
Dressing
Whisk together all ingredients for the dressing. Refrigerate until ready to serve. Give it a final whisk before pouring over salad.