  We present the first results of a survey designed to understand the origin of
the Lyman alpha-forest absorption systems at low redshift. Using the WYFFOS and
HYDRA multi-fibre spectrographs on the WHT and WIYN telescopes, we have
identified 51 galaxies brighter than b_j=18.5 within 30 arcmins of the
sightline of the QSO 1821+643. We find three galaxies within 500 h-1 kpc of the
QSO sightline; the nearest galaxy is 104 h-1 kpc away from the line of sight,
and is at the same redshift as a strong Lyman alpha absorption line. The
remaining two galaxies have no corresponding absorption to extremely low
equivalent width limits (< 0.05 \AA). Beyond 500 h-1 kpc Lyman-alpha absorption
lines are found at similar redshifts as several galaxies, but we show that
these coincidences are likely to be accidental.
  Half of the Lyman alpha systems for which we could have found at least an L^*
galaxy have no galaxies at the absorbers' redshifts. For the majority of the
remainder, we show that any apparent association with galaxies is probably
coincidental. These \lya systems are characterised by their weak equivalent
widths (W_r < 0.2 \AA), and we conclude that this population of absorbers is
uncorrelated, or at best, weakly correlated, with galaxies.
