Warm dinner plates in the oven, a plate warmer, or the microwave (make sure they are microwave safe). Peel the truffle; chop and save the peelings, then set aside. Wrap peeled truffle until ready to use.
Cut chicken breast into 4 even pieces. Season with salt and pepper, then dredge in flour. Set aside. Season the chicken before dredging, so the seasoning adheres to the meat.
Melt 2 tablespoons butter in a skillet. Add mushrooms, give a quick toss, them let them cook undisturbed for several minutes until brown. Season with salt and toss again; allow other sides to brown. Keep warm in the pan.
Place a second skillet over medium-high heat and add the remaining 1 tablespoon butter. Brown chicken, skin side down first for 3-4 minutes, then flip and sauté an additional 2-3 minutes. Remove from pan, set aside, and tent with foil to keep warm.
Deglaze pan with wine. When almost fully evaporated, add 1 cup of chicken stock. Reduce by half, and return chicken, skin side up. When chicken is cooked through, about 5 minutes, add truffle peelings, then cream. Let the sauce thicken.
Reheat the mushrooms.
Shave the truffle onto warmed plates – the plate's warmth helps to release flavour and scent without cooking the truffle – then place some cream in the middle of the plates, top with chicken, then top the chicken with mushrooms. Serve immediately.