Set the Sous Vide machine to 140 degrees Fahrenheit. It may take up to 30 minutes for it to reach that temperature.
Cut a flap halfway through each chicken breast. Lift the flap and place the pat of truffle butter under. Repeat for the other chicken breast.
Vacuum seal the chicken breasts individually in a small BPA-free sous vide safe plastic bag. Place each bag in the sous vide machine. Cook for at least 45 minutes.
Heat 1 tablespoon of vegetable oil in a large frying pan on high heat. Remove the chicken breasts from the sous vide and the vacuum sealed bags.
Crisp them in the pan for 30 seconds on each side. Set aside. Add the salted butter to the large frying pan on medium heat.
Add the shallots and the mushrooms and saute until soft and fragrant. Add the creme fraiche and stir well until boiling.
Make sure you scrape up the browned bits from the bottom of the pan.
Pour on top of the chicken breasts and serve immediately.