  Next-generation galaxy surveys will increasingly rely on the galaxy
bispectrum to improve cosmological constraints, especially on primordial
non-Gaussianity. A key theoretical requirement that remains to be developed is
the analysis of general relativistic effects on the bispectrum, which arise
from observing galaxies on the past lightcone, {as well as from relativistic
corrections to the dynamics}. {As an initial step towards a fully relativistic
analysis of the galaxy bispectrum, we compute for the first time the local
relativistic lightcone effects on the bispectrum,} which come from Doppler and
gravitational potential contributions. For the galaxy bispectrum, the problem
is much more complex than for the power spectrum, since we need the lightcone
corrections at second order. Mode-coupling contributions at second order mean
that relativistic corrections can be non-negligible at smaller scales than in
the case of the power spectrum. In a primordial Gaussian universe, we show that
the local lightcone corrections for squeezed shapes at $z\sim1$ mean that the
bispectrum can differ from the Newtonian prediction by $\gtrsim 10\%$ when the
short modes are $k\lesssim (50\,{\rm Mpc})^{-1}$. These relativistic projection
effects, if ignored in the analysis of observations, could be mistaken for
primordial non-Gaussianity. For upcoming surveys which probe equality scales
and beyond, {all relativistic lightcone effects and relativistic dynamical
corrections should be included} for an accurate measurement of primordial
non-Gaussianity.
