Make the veloute sauce by following recipe 469366. However, use chicken stock instead of veal stock, and replace half the butter with truffle oil. It will smell very strong, but when you combine it in the end the result is tempered.
Separate the chicken parts. I end up with two breasts, two wings, and two leg/thigh pieces (you could separate the legs from the thighs if you want). Save the back for making stock.
Fry the onions until slightly caramelized in a little butter. Set aside.
In the same butter (add more if needed) fry the chicken parts on both sides until firm on the outside but not browned (shouldn't take more than 30-60 seconds per side).
Place chicken parts into a baking dish in a single layer. Place the onions on top of them.
Bake at 350 for about 25 minutes. Check the temperature of the breasts. Cook further if needed. I pull them out at around 170 degrees because they'll keep cooking for a bit after you pull them out.
When breasts are cooked, pull them out, along with the wings, and place in serving bowl. Cover with foil to keep warm.
Put the thigh/legs back in the oven and cook another 10 minutes or so. They take longer to cook. Check with thermometer to see when they're done. When they're done, place them in the serving bowl and re-cover the serving bowl with foil.
Take the onions out of the baking dish and put them back in the frying pan. Add brandy and cook until brandy is reduced. Then add cream and veloute sauce and cook until it is thickened. Remove from heat and mix in butter, lemon juice, and madiera. Pour over the chicken in the serving bowl.
Serve. Escoffier recommends serving over thinly sliced truffles. Those aren't in my budget.