Place eggs in a large saucepan and fill saucepan with water until it comes to about an inch over the eggs. Place on a burner over high heat and bring to a boil. Turn off the heat, cover saucepan and let sit for 10 minutes. Once the timer goes off, transfer the eggs to an ice bath until they are cool to the touch.
Place bacon on a baking rack over a sheet pan. In a small bowl, mix together the brown sugar and cayenne with a fork. Sprinkle half of the mixture over the bacon, reserving the rest for later. Place bacon in oven, then turn oven on to 400 degrees Fahrenheit. Set a timer for 12 minutes (the preheating time is considered part of the cooking time here.)
After the 12 minutes is up, remove the bacon and, using tongs, flip it over. Sprinkle the reserved brown sugar-cayenne mixture over the second side and return to the oven for 8-10 minutes, or until the bacon looks done and fairly crisp. Remove and let cool on the rack, turning off the oven.
Peel your eggs and slice them in half vertically. Carefully scoop out the yolks and add them to a small mixing bowl. Next, add the vinegar, mayonnaise, relish, salt and pepper to the mixing bowl. Mash all of the ingredients together with a fork, until there are no large chunks remaining.
Using a piping bag, Ziploc or spoon, divide the filling evenly among the whites of the eggs. Finely chop up three slices of the candied bacon and sprinkle over the top of each egg. To finish, sprinkle on some chopped fresh chives.