Set up your sous-vide cooker with a water bath at 145°F.
Season each chicken breast with salt and pepper to taste. Put each chicken breast in a FoodSaver bag with 2 slices of lemon and a sprig of both thyme and rosemary. Vacuum seal; OR put the ingredients in a food storage bag.
When the sous vide cooker has reached 145°F add the chicken to the water bath and let it cook for between 1 1/2 to 4 hours.
When the chicken is almost done heat a cast iron or stainless steel pan over medium-high heat. Add the tablespoon of oil or butter.
Take the chicken out of the bag and throw out the lemon and herbs. Pat dry with paper towels.
Brown the chicken in the skillet for a minute or so until the chicken is nice and brown on top.
Let the chicken rest for 5 minutes or so until it is cool enough to handle.
Use your thumb to peel the chicken from the breast bone. It should come right off. Then slice the chicken diagonally and serve with lemons, capers, and herbs.
- If using frozen chicken breasts increase the cooking time to 2 1/2 hours to 4 hours. - If using boneless chicken breasts you can decrease the minimum cooking time to 1 hour.