Prepare a grill to medium heat, then add the hickory wood.
Slice the peaches in half and remove the pits. Cut in half again so the peaches are quartered.
Wrap each piece of peach in a piece of prosciutto. Hold the prosciutto in place with a soaked toothpick.
Place the prepared peaches on the preheated grill. Turn regularly, until the prosciutto begins to crisp and the peaches have caramelized a bit, 3 to 4 minutes.Tip: If you prefer a softer peach, after getting the prosciutto brown, move to the cooler side of the barbecue and allow it to continue to cook until you achieve the preferred texture.