Divide sage into four equal portions. Sprinkle one chicken breast with one portion of sage and spread two slices of prosciutto over the top.
Place the chicken breast in a heavy zip-lock bag or between two sheets of plastic wrap and, working from the center out, pound with a meat mallet (or heavy skillet) to an even thickness of about 1/4 inch. Remove from the bag or plastic wrap, taking care to not dislodge the prosciutto and sage. Repeat with remaining chicken breasts. Season to taste with salt and pepper.
Spread flour on a plate and dredge each piece of chicken lightly, shaking off excess flour.
Heat a large, heavy pan over medium high heat; cover the bottom with olive oil and heat to almost smoking. Working in two batches if necessary, add the chicken to the pan, taking care not to overcrowd. Cook until the edges begin to turn opaque, flip, and continue cooking until chicken is done through, about 6 - 8 minutes.
Drain on paper towels and serve at once.