Drill 3-inch-deep, quarter-inch-wide holes through the mortared lines in the fireplace using a hand drill. Space the holes 1 inch to 1 1/2 inches apart.
Position the pointed tip of a 3-inch wooden plug into a hole. Tap the plug gently to drive it into the hole, with its head in line with the surrounding brick surface. Install plugs in all of the holes.
Install 1-by-2-inch wood boards over the bricks. Hold each board horizontally over the bricks, with its edge flush against the closest mortar line. Drive 2-inch screws into the edges of the boards that penetrate the plugs underneath and secure them in place. Completely cover the exposed surface of the brick fireplace with the horizontal boards.
Smooth out inconsistencies, splinters and rough edges in the wood boards using medium-grit sandpaper.
Measure the dimensions of the wood surface. Transfer the measurements onto a sheet of drywall and cut it to size using a drywall saw. Dry-fit the drywall over the wood boards to cover them completely. Trim excess length along the edges using the saw.
Ask a helper to hold the drywall over the prepared surface, ensuring the boards are completely covered. Drive 2-inch drywall screws through the drywall to secure it in place.
Spread a thin layer of drywall compound over any seams in the drywall, using a putty knife. Measure and cut strips of adhesive-backed fiberglass joint tape to the length of the seams. Center each strip directly above the damp joint compound over the seam, and press it outward from the center to remove trapped air bubbles. Allow the seams to dry completely.
Apply two coats of drywall mud over the refaced area using a putty knife. Extend the second layer of drywall mud over the edges of the first layer by 4 inches to ensure a smooth transition into the surrounding wall surface. Let it cure overnight.
Sand the dried mud finish lightly to remove inconsistencies and give it a smooth finish. Depending on personal preference, paint over the repaired section or apply a coat of thin-set mortar and lay decorative tile over it.