  Primordial non-Gaussianity of the local type induces a strong scale-dependent
bias on the clustering of halos in the late-time Universe. This signature is
particularly promising to provide constraints on the non-Gaussianity parameter
$f_{\rm NL}$ from galaxy surveys, as the bias amplitude grows with scale and
becomes important on large, linear scales. However, there is a well-known
degeneracy between the real prize, the $f_{\rm NL}$ parameter, and the
(non-Gaussian) assembly bias i.e., the halo formation history-dependent
contribution to the amplitude of the signal, which could seriously compromise
the ability of large-scale structure surveys to constrain $f_{\rm NL}$. We show
how the assembly bias can be modeled and constrained, thus almost completely
recovering the power of galaxy surveys to competitively constrain primordial
non-Gaussianity. In particular, studying hydrodynamical simulations, we find
that a proxy for the halo properties that determine assembly bias can be
constructed from photometric properties of galaxies. Using a prior on the
assembly bias guided by this proxy degrades the statistical errors on $f_{\rm
NL}$ only mildly compared to an ideal case where the assembly bias is perfectly
known. The systematic error on $f_{\rm NL}$ that the proxy induces can be
safely kept under control.
