  We use an automated Voigt-profile fitting procedure to extract statistical
properties of the Ly$\alpha$ forest in a numerical simulation of an $\Omega=1$,
cold dark matter (CDM) universe. Our analysis method is similar to that used in
most observational studies of the forest, and we compare the simulations to
recently published results derived from Keck HIRES spectra. With the
Voigt-profile decomposition analysis, the simulation reproduces the large
number of weak lines ($N_{\rm HI}\la 10^{13}\cdunits$) found in the HIRES
spectra. The column density distribution evolves significantly between $z=3$
and $z=2$, with the number of lines at fixed column density dropping by a
factor $\sim 1.6$ in the range where line blending is not severe. At $z=3$, the
$b$-parameter distribution has a median of $35 \kms$ and a dispersion of $20
\kms$, in reasonable agreement with the observed values. The comparison between
our new analysis and recent data strengthens earlier claims that the \lya
forest arises naturally in hierarchical structure formation as photoionized gas
falls into dark matter potential wells. However, there are two statistically
signficant discrepancies between the simulated forest and the HIRES results:
the model produces too many lines at $z=3$ by a factor $\sim 1.5-2$, and it
produces more narrow lines ($b<20 \kms$) than are seen in the data. The first
result is sensitive to our adopted normalization of the mean \lya optical
depth, and the second is sensitive to our assumption that helium reionization
has not significantly raised gas temperatures at $z=3$. It is therefore too
early to say whether these discrepancies indicate a fundamental problem with
the high-redshift structure of the $\Omega=1$ CDM model or reflect errors of
detail in our modeling of the gas distribution or the observational procedure.
