Cut out the area of the veneer with the chip using a utility knife. You could cut out a triangle or a diamond, as long as you make simple, straight lines that you could easily replicate.
Scrape off the old glue from the furniture with the utility knife.
Place the cut piece of veneer on a new piece of veneer, adjusting the position so the grains match. Once you are happy with the grain match, tape down the cut piece of veneer.
Cut the new piece of veneer according to the shape of the old cut-out veneer piece.
Apply wood glue to both the underside of the newly cut veneer and the surface of the furniture, then put the new veneer in place. Tape it to keep it in place.
Cover the patched area with wax paper or a sheet of plastic. Clamp the patched area, wedging a block of wood under each of the two jaws of the clamp.
Remove the clamp, wax paper and wood block once the glue dries. Sand the edges of the patched area with a 120-grit sandpaper so it blends better with the surrounding area.
Apply wood stain or paint to the patched area to match the rest of the furniture.