  We investigate the degree to which the Cosmic Microwave Background (CMB) can
be used to constrain primordial non-Gaussianity coming from the presence of
spinning particles coupled to the inflaton. We compute the $\langle TTT
\rangle$ and $\langle TTTT \rangle$ correlation functions arising from the
exchange of a particle with spin $s$ and generic mass, and the corresponding
signal-to-noise ratios for a cosmic-variance-limited CMB experiment. We show
that already with \emph{Planck} data one could improve the theoretical bounds
on the amplitude of these primordial templates by an order of magnitude. We
particularly emphasize the fact that the trispectrum could be sizable even if
the bispectrum is not, making it a prime observable to explore the particle
content during inflation.
