  When inflation is driven by a pseudo-scalar field \chi coupled to vectors as
\alpha/4 \chi F \tilde F, this coupling may lead to a copious production of
gauge quanta, which in turns induces non-Gaussian and non-scale invariant
corrections to curvature perturbations. We point out that this mechanism is
generically at work in a broad class of inflationary models in supergravity
hence providing them with a rich set of observational predictions. When the
gauge fields are massless, significant effects on CMB scales emerge only for
relatively large \alpha. We show that in this regime, the curvature
perturbations produced at the last stages of inflation have a relatively large
amplitude that is of the order of the upper bound set by the possible
production of primordial black holes by non-Gaussian perturbations. On the
other hand, within the supergravity framework described in our paper, the gauge
fields can often acquire a mass through a coupling to additional light scalar
fields. Perturbations of these fields modulate the duration of inflation, which
serves as a source for non-Gaussian perturbations of the metric. In this
regime, the bounds from primordial black holes are parametrically satisfied and
non-Gaussianity of the local type can be generated at the observationally
interesting level f_NL =O(10).
