  Measurements of the non-Gaussianity of the primordial density field have the
power to considerably improve our understanding of the physics of inflation.
Indeed, if we can increase the precision of current measurements by an order of
magnitude, a null-detection would rule out many classes of scenarios for
generating primordial fluctuations. Large-scale galaxy redshift surveys
represent experiments that hold the promise to realise this goal. Thus, we
model the galaxy bispectrum and forecast the accuracy with which it will probe
the parameter $f_{\rm NL}$, which represents the degree of primordial
local-type non Gaussianity. Specifically, we address the problem of modelling
redshift space distortions (RSD) in the tree-level galaxy bispectrum including
$f_{\rm NL}$. We find novel contributions associated with RSD, with the
characteristic large scale amplification induced by local-type non-Gaussianity.
These RSD effects must be properly accounted for in order to obtain un-biased
measurements of $f_{\rm NL}$ from the galaxy bispectrum. We propose an analytic
template for the monopole which can be used to fit against data on large
scales, extending models used in the recent measurements. Finally, we perform
idealised forecasts on $\sigma_{f_{\rm NL}}$ -- the accuracy of the
determination of local non-linear parameter $f_{\rm NL}$ -- from measurements
of the galaxy bispectrum. Our findings suggest that current surveys can in
principle provide $f_{\rm NL}$ constraints competitive with Planck, and future
surveys could improve them further.
