Place eggs in a single layer in a large pot (do not stack eggs). Add enough cold water to cover eggs by 1 inch. Bring to boiling. Turn off heat and let stand 10 minutes; drain. Run cold water over eggs or place them in ice water until cool enough to handle; drain.
Peel eggs and halve lengthwise. Remove yolks to a medium bowl. Place whites, cut sides up, on a large platter.
Beat yolks, mayonnaise, cream cheese, and mustard with a mixer on medium until smooth. Stir in chives and salmon. Stuff egg white halves with yolk mixture. If desied, top with additional chives.