Mix soy sauce and sesame oil in a bowl; rub mixture over chicken breasts. Season with salt and pepper.
Heat a large skillet over medium heat; cook marinated chicken in the hot skillet until no longer pink in the center and juices run clear, about 20 minutes. Dice chicken when cool enough to handle and transfer to a large bowl.
Combine water, long grain and wild rice mix, and butter in a saucepan; bring to a boil. Reduce heat, cover pan, and simmer until rice is tender and liquid is absorbed, about 25 minutes.
Mix rice, mandarin oranges, water chestnuts, green onion, celery, and almonds with diced chicken; toss well. Chill mixture in refrigerator for at least 15 minutes.
Line a large platter with lettuce leaves; top with chicken mixture. Sprinkle noodles around salad.