In 4-quart saucepan or Dutch oven, place eggs in single layer. Add enough water to cover eggs by 1 inch. Heat to boiling. Immediately remove from heat; cover and let stand 15 minutes. Drain; rinse with cold water. Place eggs in bowl of ice water; let stand 10 minutes.
To remove shell, crack it by tapping gently all over; roll between hands to loosen. Peel, starting at large end.
Cut eggs lengthwise in half. Into medium bowl, slip out yolks; mash with fork. Stir dressing mix, mayonnaise and mustard into yolks.
Spoon or pipe yolk mixture into egg white halves. Sprinkle with chives. Refrigerate at least 30 minutes before serving.