  We propose that a large fraction of the QSO Lyman limit absorption systems
(LLS) observed at high redshift (z > 3) originate from gas trapped in small
objects, such as minihalos, that form prior to reionization. In the absence of
a strong UV flux, the gas is predominantly neutral and may form clouds with HI
column density NHI > 10^18 cm^-2. Due to their high densities and high HI
column densities, these clouds are not destroyed by the onset of the UV
background at a later time. Thus, if not disrupted by other processes, such as
mergers into larger systems or `blow away' by supernovae, they will produce
LLS. We show that the observed number density of LLS at high redshifts can well
be reproduced by the survived `minihalos' in hierarchical clustering models
such as the standard cold dark matter model. The number density of LLS in such
a population increases with z even beyond the redshifts accessible to current
observations and dies off quickly at z < 2. This population is distinct from
other populations because the absorbing systems have small velocity widths and
a close to primordial chemical composition. The existence of such a population
requires that the reionization of the universe occurs late, at z < 20.
