  We determine the abundance of primordial black holes (PBHs) formed in the
context of non-gaussian models with primordial density perturbations. We
consider models with a renormalized $\chi^2$ probability distribution function
parametrized by the number, $\nu$, of degrees of freedom. We show that if $\nu$
is not too large then the PBH abundance will be altered by several orders of
magnitude with respect to the standard gaussian result obtained in the $\nu \to
\infty$ limit. We also study the dependence of the spectral index constraints
on the nature of the cosmological perturbations for a power-law primordial
power spectrum.
