Put the eggs in a large pot and add enough water to cover by about 1 inch. Bring the pot to boil (BTB), cover and then turn off the heat and let sit for 13 minutes EXACTLY!
Drain the eggs and run them under cold water until cool; if you're not using them right away, put them in the fridge.
Peel the eggs and cut them in half lengthwise. Remove the yolks. Put the yolks in a small bowl and mash them with a fork. Add the mayonnaise, truffle peeling, truffle oil and cayenne and whip until very light and fluffy.
Use a disposable pastry bag (or just buy zip-top bags, fill them and cut off one corner - a very low-tech solution but my favorite kind!) to pipe the yolk mixture into the whites (or just spoon it in). Sprinkle with the chives to serve.
Want to goose up the truffle-y flavor? Add a dash more truffle oil. But proceed with caution: it's very easy to over truffle!