Fireplaces, Heating Stoves, Flues and Chimneys - stone fireplace mod

We have a stone fireplace that extends the entire width of the room and halfway up to the ceiling. I have been wanting to buy a pre-fab surround and cover over the stone with drywall. What I was thinking was using some thin lumber (how thin?) and framing up a "false wall" all around the fireplace and drywalling that. Then install the new surround, leaving a border of the original stone showing on the inside. (so it still ties in to the giant stone hearth that also stretches the entire width of the room). What I want to know is how to I fasten this lumber and/or drywall to the original stone? Is there any way I can avoid having to fasten anything to the stone?