Start by placing large eggs in a pot and covering them with cold water. Bring the pot to a rapid boil over medium-high heat, then cover it and let it sit off the heat for 12 minutes.

Transfer the eggs to an ice water bath for about 10 minutes to cool.

Peel the eggs under running water, starting from the larger end.

Slice each egg in half lengthwise and remove the yolks to a mixing bowl. Mash the yolks and add mayonnaise, mustard, vinegar, salt, and pepper. Mix until creamy.

Divide the yolk mixture into separate bowls and add food coloring to each as desired.

Fill the egg whites with colored yolk mixtures using a spoon or piping bag. Decorate with black olives and chives.

Refrigerate the deviled eggs for at least 30 minutes before serving.