Combine mayonnaise, green onions, and, if desired, chives, chill.
Combine chicken, mango, tomato, and green pepper in a large bowl.
Combine oil, vinegar, lemon juice, and sugar in a jar.
Cover and shake vigorously.
Pour over chicken mixture, chill at least 30 minutes.
Spoon chicken salad mixture onto a lettuce-lined plate.
Top with mayonnaise mixture.