  Recent tentative findings of non-Gaussian structure in the COBE-DMR dataset
have triggered renewed attention to candidate models from which such intrinsic
signature could arise. In the framework of slow roll inflation with built-in
non linearities in the inflaton field evolution we present expressions for both
the cosmic microwave background (CMB) skewness and the full angular bispectrum
${\cal C}_{\ell_1 \ell_2 \ell_3}$ in terms of the slow roll parameters. We use
an estimator for the angular bispectrum recently proposed in the literature and
calculate its variance for an arbitrary $\ell_i$ multipole combination. We
stress that a real detection of non-Gaussianity in the CMB would imply that an
important component of the anisotropies arises from processes {\it other} than
primordial quantum fluctuations. We further investigate the behavior of the
signal-to-(theoretical) noise ratio and demonstrate for generic inflationary
models that it decreases in the limited range of small-$\ell$'s considered for
increasing multipole $\ell$ while the opposite applies for the standard ${\cal
C}_{\ell}$'s.
