Apply several layers of paint to the quarter round and allow it to dry.
Measure the distance from the floor to the top of the fireplace or the ceiling if the fireplace chimney extends to the top of the wall. Since most ceilings in homes built before the mid-90s are 8 feet tall, and molding comes in 8-foot lengths, no cutting may be necessary.
Use heavy shears to cut the quarter round the appropriate length. If you intend to place molding around a fireplace that doesn't reach the ceiling, use a miter saw and box to cut the top edge at a 45-degree angle, with the outside edge of the molding higher than the inside edge when it's in place. Make the cut with as few strokes of the saw as possible so the quarter round doesn't melt or split.
Insert a tube of construction adhesive into a caulk gun and cut off the tip. Run a bead of adhesive along the two flat sides of the molding. Press the molding into place along the side of the fireplace. Repeat the process on the other side of the fireplace. Wipe up excess glue with a damp cloth before it hardens.
Measure the top of the fireplace if the fireplace doesn't run all the way to the ceiling. Cut a piece of molding to fit between the tops of the side pieces and then cut each end of the top piece at a 45-degree angle. Run a bead of glue along the inside of the top piece and press it into place between the two side pieces.