Create a Temporary Brace
At the fire-box opening, use a scrap piece of 2x4 as a temporary brace to hold up the stack stone until it cures. Cut a piece to the width of the opening and two more pieces to the height of the opening, minus 1-3/4". Hold the first piece up to the top of the opening, then place the other two into position to hold it up.
Once all the stone is applied, wipe off any excess mortar on the stone. After the mortar has cured, remove the scrap wood.
Note: Unlike veneer stone, stacked stone does not have mortar joints to fill.