Place chicken breasts in a bowl, pour teriyaki sauce over them, and coat well. Cover, and refrigerate for 1 hour.
Preheat an outdoor grill for direct heat.
For the dressing, place green onions, salt, pepper, and sugar in a blender. Pour in olive oil and rice vinegar. Blend until smooth. Remove to a bowl, cover, and refrigerate until ready to serve.
Grill chicken, turning, until done. Remove to a cutting board, and cut into strips.
In a large skillet or wok, warm oil over medium-high heat. Cut wonton wrappers into strips. Fry wonton strips until crisp. Remove to paper towels.
In a large bowl, toss together lettuce, water chestnuts, sesame seeds, sliced almonds, and mandarin oranges. Pour dressing over salad, and toss gently. Top with fried wontons and grilled chicken strips.
