  We use new observations of very weak CIV absorption lines associated with
high-redshift Lyman-alpha absorption systems to measure the high-redshift
Lyman-alpha line two-point correlation function (TPCF). These very weak CIV
absorption lines trace small-scale velocity structure that cannot be resolved
by Lyman-alpha absorption lines. We find that (1) high-redshift Lyman-alpha
absorption systems with N(HI) > 3.10^14 cm^{-2} are strongly clustered in
redshift, (2) previous measurements of the Lyman-alpha line TPCF underestimated
the actual clustering of the absorbers due to unresolved blending of
overlapping velocity components, (3) the present observations are consistent
with the hypothesis that clustering of Lyman-alpha absorption systems extends
to lower column densities, but maybe with smaller amplitude in the correlation
function, and (4) the observed clustering is broadly compatible with that
expected for galaxies at z \sim 2-3. We interpret these results as suggesting
that many or most Lyman-alpha absorbers may arise in galaxies even at high
redshifts, and, therefore, that the Lyman-alpha forest probes processes of
galaxy formation and evolution for redshifts \lesssim 5.
