Place eggs in a saucepan and cover with cold water; bring to a rolling boil; boil 10 minutes. Remove from heat, drain, and run very cold water over the eggs.
Peel eggs and halve; remove yolks and mash in a bowl with a fork.
Mix drained tuna, mayonnaise, celery, green onions and relish; stir into mashed yolks and mix until smooth.
Fill egg cavities with filling mixture and garnish with snipped chives.