First, set up your sous-vide water bath and preheat it to 60°
Pat the chicken breasts dry with paper towels. Season them generously with salt and black pepper.
Place each chicken breast in a vacuum-sealable bag with a rosemary sprig and a tiny drizzle of olive oil. Seal the bags, ensuring as much air as possible is removed.
Finely chop the shallot for the Béarnaise sauce. Melt the butter in a small saucepan over low heat without browning, then skim off the foam and carefully pour the clear butter into a separate bowl, leaving the milk solids behind (this is clarified butter).
Chop the fresh tarragon and chervil (if using) and set aside.