  The intense UV radiation from a highly luminous QSO should excite fluorescent
Ly-alpha emission from any nearby neutral hydrogen clouds. We present a very
deep narrow-band search for such emission near the z=2.168 quasar PKS 0424-131,
obtained with the Taurus Tunable Filter on the Anglo-Australian Telescope. By
working in the UV, at high spectral resolution and by using charge shuffling,
we have been able to reach surface brightness limits as faint as 4.7E-19
erg/cm^2/s/arcsec^2.
  No fluorescent Ly-alpha emission is seen, whereas QSO absorption-line
statistics suggest that we should have seen ~6 clouds, unless the clouds are
larger than ~ 100 kpc in size. Furthermore, we do not even see the normal
population of Ly-alpha emitting galaxies found by other surveys at this
redshift. This is very different fromobservations of high redshift radio
galaxies, which seem to be surrounded by clusters of Ly-alpha emitters. We
tentatively conclude that there is a deficit of neutral hydrogen close to this
quasar, perhaps due to the photo-evaporation of nearby dwarf galaxies.
