Place a sheet or plastic in front of the fireplace to avoid getting soot on the floor. Remove the fireplace grate and clean out the firebox. Lay a sheet on the floor of the firebox.
Put the end of your tape measure on the edge of the chimney's mouth (i.e., the interior opening above the fireplace that leads up to the chimney, not the hearth opening) on the center of one side. Measure up 3 inches and make a mark. Repeat for the remaining three sides.
Position an angle bracket at one of the marks, with the top of the bracket even with the mark. Mark the mounting hole for the bracket and repeat for the remaining three sides.
Drill 1-inch-deep pilot holes at each mounting bracket hole with a masonry bit that's slightly smaller than the concrete screws. Line up each mounting bracket with a pilot hole and secure it with a concrete screw and a cordless screwdriver with a socket adapter.
Measure the chimney's mouth opening with a tape measure. If you have a throat damper, measure the mouth of the chimney 6 inches below the damper mounts. Cut a piece of 3/4-inch-thick plywood to the measurement with a circular saw.
Slide the piece of plywood past the mounting brackets in the chimney, then gently lower it over the brackets. Apply a bead of silicone caulk around the edge of the plywood where it meets the sides of the chimney with a caulk gun.