  This paper explores the consequences of non-Gaussian cosmological
perturbations for the formation of primordial black holes (PBHs). A
non-Gaussian probability distribution function (PDF) of curvature perturbations
is presented with an explicit contribution from the three-point correlation
function to linear order. The consequences of this non-Gaussian PDF for the
large perturbations that form PBHs are then studied. Using the observational
limits for the non-Gaussian parameter $f_{NL}$, new bounds to the mean
amplitude of curvature perturbations are derived in the range of scales
relevant for PBH formation.
