  Cosmological simulations with gas provide a detailed description of the
intergalactic medium, making possible predictions of neutral hydrogen
absorption in the spectra of background QSOs. We present results from a
high-resolution calculation of an $\Omega=1$ cold dark matter model. Our
simulation reproduces many of the observed properties of the \lya forest
surprisingly well. The distribution of HI column densities agrees with existing
data to within a factor of $\sim$ two over most of the range from
$10^{14}\cm^{-2}$ to $10^{22}\cm^{-2}$; i.e., from unsaturated \lya forest
lines to damped \lya systems. The equivalent width distribution matches the
observed exponential form with a characteristic width $W_* \approx 0.3$
angstroms. The distribution of b-parameters appears consistent with that
derived from QSO spectra. Most of the low column density absorption arises in
large, flattened structures of moderate or even relatively low overdensity, so
there is no sharp distinction between the \lya forest and the ``Gunn-Peterson''
absorption produced by the smooth intergalactic medium. Our results demonstrate
that a \lya forest like that observed develops naturally in a hierarchical
clustering scenario with a photoionizing background. Comparison between
simulations and high-resolution QSO spectra should open a new regime for
testing theories of cosmic structure formation.
