  We examine large-scale fluctuations in the HeII Lyman-alpha forest
transmission during and after HeII reionization. We use a simple Monte Carlo
model to distribute quasars throughout a large volume and compute the resulting
radiation field along one-dimensional skewers. In agreement with previous
studies, we find that the rarity of these sources induces order unity
fluctuations in the mean optical depth after reionization, even when averaged
over large segments (~10-100 Mpc across). We compare our models to existing
data along five HeII Lyman-alpha forest lines of sight spanning z~2-3.2. The
large cosmic variance contained in our model plausibly explains many of the
observed fluctuations at z<2.5. But our models cannot accommodate the large
fluctuations toward high optical depths on ~30 Mpc scales observed at
z~2.7-2.9, and the measured optical depths (tau>4) at z>2.9 are difficult to
explain with a smoothly-evolving mean radiation field. In order to better
understand this data, we construct a toy model of HeII reionization, in which
we assume that regions with the smallest radiation fields in a
post-reionization Universe (or farthest from strong ionizing sources) are
completely dark during reionization. The observed fluctuations fit much more
comfortably into this model, and we therefore argue that, according to present
data, HeII reionization does not complete until z<2.9.
