Preheat oven to 400°. Using a meat tenderizer, pound the chicken until 1/4" thick. Pat dry and liberally season it with salt and pepper on both sides. Place a spoonful or two of Boursin on one end of each piece, top with a sprinkle of mozzarella cheese, and roll the chicken up, starting at the cheese-topped end. Wrap chicken with a slice of prosciutto and place in a baking dish seam-side down, so the prosciutto doesn't unravel. Repeat with each piece of chicken.
Bake for 30 to 35 minutes, or until chicken is no longer pink and juices run clear when pierced with a fork or knife.