Place chicken breasts onto a sheet of parchment paper. Place a prosciutto slice and a sage leaf onto each breast. Roll chicken from the short end over prosciutto and secure with wooden skewers.

Melt butter in a skillet over medium-high heat. Add rolled chicken and cook until well browned, 2 to 3 minutes per side. Add wine, salt, and pepper; cook until chicken is no longer pink in the center, 8 to 10 minutes. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C). Let rest for 5 minutes before serving.