To make the pickling mixture, combine borscht and vinegar in a container. Add eggs to borscht mixture, making sure they are completely covered. Cover and refrigerate for 12 hours, or up to 2 days.  Remove eggs from the liquid. Cut each egg in half lengthwise, gently removing yolks and placing them in a bowl. Place whites on a serving platter, and set aside. Mash yolks well with a fork. Add mayonnaise, mustard, onion powder, salt, and pepper to taste. Spoon the yolk filling into the egg whites; or for a prettier presentation, pipe them in using a pastry bag with a star tip. Garnish with chives.