Place eggs in a large pot and cover with cold water by 1 inch. Bring to a boil over high heat, then remove from heat, cover, and let sit for 12 minutes.
Transfer eggs to an ice bath and let them cool for at least 5 minutes. This makes peeling so much easier!
Peel the eggs and slice them in half lengthwise. Carefully scoop out the yolks into a medium bowl.
Mash the yolks with a fork until smooth, then add mayonnaise, mustard, vinegar, salt, and pepper. Mix until creamy and well combined.
Spoon or pipe the yolk mixture into the egg white halves. A plastic bag with the corner snipped off works great if you don't have a piping bag!
Sprinkle with paprika and garnish with chopped chives if desired. Refrigerate until ready to serve.