Gather all your ingredients.
Season the chicken breasts with a generous sprinkle of kosher salt and a dash of freshly ground black pepper. Lay two sage leaves on each chicken breast, pressing them slightly to help them adhere. Place a slice of prosciutto on top of each breast, trimming the edges if needed to fit snugly. Press the prosciutto down to secure it to the chicken.
Lightly coat each piece of chicken with all-purpose flour, shaking off any excess.
Heat a large skillet over medium-high heat and add the olive oil along with 2 tablespoons of the butter. Once the butter has melted and the oil is hot, place two of the chicken breasts in the skillet, prosciutto side facing up. Cook for about 3 minutes until the chicken is nearly cooked through.
Carefully flip the chicken over and continue to cook for an additional minute, just until the prosciutto begins to tighten up. Remove the chicken from the skillet and set it aside on a plate. Repeat this process with the remaining chicken breasts. After removing the last pieces, discard any remaining fat from the skillet and wipe it clean.
Return the skillet to the heat and add the remaining 2 tablespoons of butter.
Pour in the white wine, and bring it to a boil, allowing it to reduce by half, which should take around 2 minutes.
Next, add the chicken stock, and bring the mixture to a rolling boil. Allow it to reduce by half again, which will take another 3 minutes.
Place the chicken breasts back into the skillet, prosciutto side facing up. Let them simmer gently over medium heat until fully cooked, which should take about 2 minutes. Adjust the seasoning with additional salt and pepper if needed. Serve the chicken on plates, spoon the sauce over the top, and enjoy your Chicken Saltimbocca.