Lay a drop cloth around the fireplace to protect flooring from pieces of mortar and brick that may fall. Set the stepladder on a flat place on the floor.
Set the edge of the chisel on the mortar next to the top right brick on the fireplace facade. Use the mallet to hit the end of the chisel, driving it into the mortar. After three or four strikes, you should see the mortar start to crack.
Slide the chisel over to another space on the mortar around the brick. Hit the end of the chisel as you move it around the first brick.
Pry the brick out with the chisel. Move to the next brick along the top of the facade and repeat the hammering. Work from the top of the fireplace facade to the last row of bricks you want to remove.
Chisel off any large chunks of mortar that are attached to the wall in preparation for refacing the surface.