  Following the completion of cosmic reionization, the mean-free-path of
ionizing photons was set by a population of Ly-limit absorbers. As the
mean-free-path steadily grew, the intensity of the ionizing background also
grew, thus lowering the residual neutral fraction of hydrogen in ionization
equilibrium throughout the diffuse intergalactic medium (IGM). Ly-alpha photons
provide a sensitive probe for tracing the distribution of this residual
hydrogen at the end of reionization. Here we calculate the cosmic variance
among different lines-of-sight in the distribution of the mean Ly-alpha optical
depths. We find fractional variations in the effective post-reionization
optical depth that are of order unity on a scale of ~100 co-moving Mpc, in
agreement with observations towards high-redshift quasars. Significant
contributions to these variations are provided by the cosmic variance in the
density contrast on the scale of the mean-free-path for ionizing photons, and
by fluctuations in the ionizing background induced by delayed or enhanced
structure formation. Cosmic variance results in a highly asymmetric
distribution of transmission through the IGM, with fractional fluctuations in
Ly-alpha transmission that ar larger than in Ly-beta transmission.
