Add the chopped beet to a pot with the 3 cups water, apple cider vinegar, salt and sugar. Bring it to a boil then reduce the heat, cover the pot and let it simmer for about 25-30 minutes.
Let the mixture cool completely then transfer it to a bowl. Submerge the peeled hard boiled eggs in the beet juice, making sure they're fully covered. Refrigerate for 3-4 hours, or even overnight if prepared ahead of time. The longer they sit, the richer the color and pickled flavor. I chilled mine for 4 hours.
To prepare the deviled eggs, remove the eggs from the beet juice and slice them in half lengthwise. Remove the yolks and add them to a bowl with the mayonnaise, mustard, chives, and a pinch of salt u0026 pepper to taste. Mash together until smooth.
Transfer the yolk mix into a ziplock bag with a hole cut in the bottom corner, or piping bag, and fill each half of the eggs. You can also use a small spoon to scoop the mix into each egg half. Garnish with fresh chives, dill and crushed black pepper
Leftovers can be refrigerated for up to 4 days and served cold or at room temperature.