  After the precise observations of the Cosmic Microwave Background (CMB)
anisotropy power spectrum, attention is now being focused on the higher order
statistics of the CMB anisotropies. Since linear evolution preserves the
statistical properties of the initial conditions, observed non-Gaussianity of
the CMB will mirror primordial non-Gaussianity. Single field slow-roll
inflation robustly predicts negligible non-Gaussianity so an indication of
non-Gaussianity will suggest alternative scenarios need to be considered. In
this paper we calculate the information on primordial non-Gaussianity encoded
in the polarization of the CMB. After deriving the optimal weights for a cubic
estimator we evaluate the Signal-to-Noise ratio of the estimator for WMAP,
Planck and an ideal cosmic variance limited experiment. We find that when the
experiment can observe CMB polarization with good sensitivity, the sensitivity
to primordial non-Gaussianity increases by roughly a factor of two. We also
test the weakly non-Gaussian assumption used to derive the optimal weight
factor by calculating the degradation factor produced by the gravitational
lensing induced connected four-point function. The physical scales in the
radiative transfer functions are largely irrelevant for the constraints on the
primordial non-Gaussianity. We show that the total (S/N)^2 is simply
proportional to the number of observed pixels on the sky.
