Place chicken breasts on work surface. Using sharp knife and starting at thickest side of 1 chicken breast, cut 2-inch-long, 1-inch-deep horizontal pocket, being careful not to cut through completely to other side of breast. Insert 1 piece of cheese in pocket and press opening closed. Sprinkle chicken with salt and pepper. Place 2 prosciutto slices side by side on work surface, slightly overlapping on long sides. Place 1 chicken breast crosswise atop center of prosciutto slices; wrap prosciutto slices around chicken, covering completely and pressing to adhere (if necessary, fasten with small turkey skewers). Repeat with remaining chicken, cheese, and prosciutto. DO AHEAD Can be made 6 hours ahead. Cover and chill.