  (ABRIDGED)The rise of cosmic structure depends upon the statistical
distribution of initial density fluctuations generated by inflation. While the
simplest models predict an almost perfectly Gaussian distribution, more-general
models predict a level of primordial non-Gaussianity (PNG) that observations
might yet be sensitive enough to detect. Recent Planck Collaboration
measurements of the CMB temperature anisotropy bispectrum significantly tighten
the observational limits, but they are still far from the PNG level predicted
by the simplest models of inflation. Probing levels below CMB sensitivities
will require other methods, such as searching for the statistical imprint of
PNG on galactic halo clustering. During the epoch of reionization (EoR), the
first stars and galaxies released radiation into the intergalactic medium (IGM)
that created ionized patches whose large-scale geometry and evolution reflected
the underlying abundance and large-scale clustering of the star-forming
galaxies. This statistical connection between ionized patches in the IGM and
galactic halos suggests that observing reionization may be another way to
constrain PNG. We employ the linear perturbation theory of reionization and
semi-analytic models based on the excursion-set formalism to model the effects
of PNG on the EoR. We quantify the effects of PNG on the large-scale structure
of reionization by deriving the ionized density bias, i.e. ratio of ionized
atomic to total matter overdensities in Fourier space, at small wavenumber.
Just as previous studies found that PNG creates a scale-dependent signature in
the halo bias, so, too, we find a scale-dependent signature in the ionized
density bias. Our results, which differ significantly from previous attempts in
the literature to characterize this PNG signature, will be applied elsewhere to
predict its observable consequences, e.g. in the cosmic 21cm background.
