Rinse and pat dry chicken breast halves and place them smooth-side up on a work surface. Place four sage leaves at an angle atop each chicken breast half, spacing them evenly for a uniform, striped look. Carefully center a prosciutto slice atop the chicken breast widthwise, covering sage leaves, and wrap the slice around, securing it in back with toothpicks.
In a nonstick skillet, heat olive oil on medium. Place chicken breasts sage-side down in pan, cover and cook 10 minutes. Turn chicken breasts and continue cooking, uncovered, until cooked though, 5-7 minutes depending on thickness.
Transfer chicken breasts to dinner plates. Add sherry to pan and increase heat to medium-high. Cook, scraping to loosen any browned bits, for 1 minute, until liquid in pan becomes a syrupy glaze. Place each chicken breast half on a dinner plate, spoon some pan glaze over each and serve immediately.