  We use redshift-space galaxy clustering data from the BOSS survey to
constrain local primordial non-Gaussianity (LPNG). This is of particular
importance due to the consistency relations, which imply that a detection of
LPNG would rule out all single-field inflationary models. Our constraints are
based on the consistently analyzed redshift-space galaxy power spectra and
bispectra, extracted from the public BOSS data with optimal window-free
estimators. We use a complete perturbation theory model including all one-loop
power spectrum corrections generated by LPNG. Our constraint on the amplitude
of the local non-Gaussian shape is $f_{\rm NL}^{\rm local}=-33\pm 28$ at
68\%\,CL, yielding no evidence for primordial non-Gaussianity. The addition of
the bispectrum tightens the $f_{\rm NL}^{\rm local}$ constraints from BOSS by
$20\%$, and allows breaking of degeneracies with non-Gaussian galaxy bias.
These results set the stage for the analysis of future surveys, whose larger
volumes will yield significantly tighter constraints on LPNG.
