Pierce chicken thighs with a fork all over. In a gallon size bag or large bowl, combine chicken and teriyaki sauce; marinate for at least 1 hour to overnight, turning the bag occasionally. Drain the chicken from the marinade.
In a small bowl, whisk together peanut butter, soy sauce, apple cider vinegar, brown sugar, garlic and 1/4 cup warm water until smooth. If the dressing is thin, add a little more peanut butter. Place in the refrigerator until ready to serve.
Preheat grill to medium heat.
Brush drained chicken with canola oil; season with salt and pepper, to taste. Add to grill, and cook, turning occasionally, until chicken is completely cooked through, reaching an internal temperature of 165 degrees F, about 10 minutes.
To assemble the salad, place romaine lettuce in a large bowl; top with cabbage, carrots, mandarin oranges, chicken, peanuts, cilantro and green onions. Pour the peanut dressing on top of the salad and gently toss to combine.