Cut the cheese into 6 equal portions. Top each piece of cheese with two sage leaves and wrap with a slice of ham.
Place each cheese bundle on one side of a butterflied chicken breast. Fold the chicken over to enclose the filling and secure closed with toothpicks.
Sprinkle evenly with salt and pepper.
Chop the remaining sage. Stir the ketchup with the balsamic vinegar, maple syrup, mustard, garlic and chopped sage until combined. Divide glaze in half.
Brush one portion over the chicken.
Place the chicken on the grill and reduce the temperature to medium. Grill the chicken for 6 minutes; turn and baste with the remaining sauce. Grill for an additional 10 minutes, or until an instant read thermometer inserted into the thickest portion of meat registers 165 degrees F (74 degrees C).
Remove from grill, tent with foil and let rest for 5 minutes. Slice meat thickly and fan to serve.
