Find the studs behind the wallboard using a stud finder and clearly mark them. Position a 1-by-18-by-18-inch board against the wall so it lines up on a stud, with the bottom edge of the board 20 inches off the ground. Place a carpenter's level on top of the board and adjust it until it is straight. Drill holes through the board and into the stud every 4 inches. Attach the board to the wall with 4-inch wood screws passed through washers.
Press a long, thin side of another 1-by-18-by-18-inch board against the front surface of the wall board. Slide the horizontal board down the vertical board until the bottom surface of the horizontal board is flush with the bottom edge of the vertical board. Set three heavy-duty door hinges on the top of the horizontal board, against the vertical board. Mark the position of the hinge screw attachment holes on both boards.
Remove the hinges and drill out the holes in both boards. Reposition the hinges and the boards and attach the hinge in place with 1-inch wood screws to the horizontal board and 4-inch wood screws to the vertical board.
Position an 18-inch, 2-by-4 support board underneath the chair so the 4-inch side presses up against the bottom of the vertical board and the bottom edge of the horizontal board. Press a 2-inch edge of the 2-by-4 against the wall. Drill four holes down through the horizontal board and into the 2-by-4. Attach the 2-by-4 to the horizontal board with 2-inch wood screws drilled down through the horizontal board and into the 2-by-4.