  Next-generation galaxy and 21cm intensity mapping surveys will rely on a
combination of the power spectrum and bispectrum for high-precision
measurements of primordial non-Gaussianity. In turn, these measurements will
allow us to distinguish between various models of inflation. However, precision
observations require theoretical precision at least at the same level. We
extend the theoretical understanding of the galaxy bispectrum by incorporating
a consistent general relativistic model of galaxy bias at second order, in the
presence of local primordial non-Gaussianity. The influence of primordial
non-Gaussianity on the bispectrum extends beyond the galaxy bias and the dark
matter density, due to redshift-space effects. The standard redshift-space
distortions at first and second order produce a well-known primordial
non-Gaussian imprint on the bispectrum. Relativistic corrections to
redshift-space distortions generate new contributions to this primordial
non-Gaussian signal, arising from: (1)~a coupling of first-order
scale-dependent bias with first-order relativistic observational effects, and
(2)~linearly evolved non-Gaussianity in the second-order velocity and metric
potentials which appear in relativistic observational effects. Our analysis
allows for a consistent separation of the relativistic `contamination' from the
primordial signal, in order to avoid biasing the measurements by using an
incorrect theoretical model. We show that the bias from using a Newtonian
analysis of the squeezed bispectrum could be $\Delta \fnl\sim 5$ for a Stage IV
H$\alpha$ survey.
