Sandwich the boneless, skinless chicken breasts between two slices of waxed paper. Flatten each chicken breast by pounding with a mallet or the bottom of a heavy frying pan or other heavy object.
Place a piece of ham or prosciutto on each chicken breast and roll. Place seam side down in a shallow baking dish. Mix together catsup, mayonnaise and jam.
Pour mixture over the chicken. Bake uncovered in a 350 degrees Fahrenheit for 20-25 minutes.