Place the eggs in a saucepan, cover with water, bring to a boil, then remove from the heat, cover, and let stand for 10 minutes. Cool in ice water and peel.
Halve the eggs lengthwise and carefully remove the yolks. Mash the yolks in a bowl until smooth.
Stir in the mayonnaise, celery, tomato juice, horseradish, lemon juice, Worcestershire sauce, hot pepper sauce, celery salt, and black pepper until creamy.
Spoon or pipe the yolk mixture into the egg-white halves. Garnish with chopped chives and chill until ready to serve.
Notes
For the cleanest filling, mash the yolks thoroughly before adding the wet ingredients.