Set up a water bath and immersion circulator according to manufacturer’s instructions. Bring water to 143 degrees F (62 degrees C).
Place chicken, oil, herbes de Provence, garlic paste, salt, and lemon zest in a bowl. Mix until coated. Place in the vacuum bag in a single layer; seal.
Submerge bagged chicken in the water bath and cook for 3 hours. Cool chicken in the sealed bag under cold running water.