Preheat the oven to 475 degrees F. Rinse the chicken well inside and out and pat dry with paper towels.

Drain the truffles and reserve liquid separately. Slice the truffles thinly and reserve the nicest 8 or 10 slices. Set the remaining truffle slices aside.

Working carefully, loosen the skin on the breasts of the chicken and insert the slices of truffle between the breast and the skin. Season the chicken well both inside and out with salt and pepper and tie the legs together. Turn the wings under the bird. Heat a Dutch oven just large enough to hold the chicken with 2 tablespoons olive oil. Scatter the onion, celery, and carrot over the bottom of the Dutch oven. Rub the chicken on all sides with 1 tablespoon of the butter and add the chicken to the Dutch oven on its side. Add the Champagne. Place the Dutch oven in the oven and cook the chicken, undisturbed, for 20 minutes, until golden brown on the side facing up. Carefully turn the chicken to its other side and baste with the drippings and continue to cook until golden brown on the second side, about 15 minutes longer. Finally, reduce the oven temperature to 375 degrees F and turn the chicken on its back. Continue to cook the chicken until golden brown on the breast side and the juices run clear when pieced in the deepest part of the thigh, 30 to 40 minutes longer. Transfer chicken to a platter and keep warm.

Transfer the Dutch oven to the stovetop and heat over medium-high heat. Skim as much of the fat from the drippings as possible and discard fat. Add the white wine and cook, stirring to dissolve the browned bits stuck to the inside of the pan. Add the chicken broth and truffle juice and continue to cook until the liquid has reduced by about 50 percent. While the broth is reducing, combine the remaining 2 tablespoons of butter and the flour in a small bowl and, using the back of a spoon, make a smooth paste. When the liquid has reduced by 50 percent, strain through a fine-meshed sieve and return to the Dutch oven or to a clean saucepan. Add the heavy cream and reserved truffle slices and bring to a simmer. Ladle about 1/2 cup of the hot mixture into the small bowl with the butter-flour mixture and whisk until smooth. Slowly whisk the butter-flour mixture into the sauce in the saucepan and continue to cook until sauce is thick enough to coat the back of a spoon and flavorful, about 10 minutes. Season, to taste, with salt and white pepper. Add any accumulated juices from the resting chicken to the sauce, cut the chicken into serving pieces and serve, with the sauce ladled over the chicken.