  We describe a new numerical algorithm to obtain high-resolution simulated
maps of the Cosmic Microwave Background (CMB), for a broad class of
non-Gaussian models. The kind of non-Gaussianity we account for is based on the
simple idea that the primordial gravitational potential is obtained by a
non-linear but local mapping from an underlying Gaussian random field, as
resulting from a variety of inflationary models. Our technique, which is based
on a direct realization of the potential in spherical coordinates and fully
accounts for the radiation transfer function, allows to simulate non-Gaussian
CMB maps down to the Planck resolution ($\ell_{\rm max} \sim 3,000$), with
reasonable memory storage and computational time.
