  We study the peculiar velocities of density peaks in the presence of
primordial non-Gaussianity. Rare, high density peaks in the initial density
field can be identified with tracers such as galaxies and clusters in the
evolved matter distribution. The distribution of relative velocities of peaks
is derived in the large-scale limit using two different approaches based on a
local biasing scheme. Both approaches agree, and show that halos still stream
with the dark matter locally as well as statistically, i.e. they do not acquire
a velocity bias. Nonetheless, even a moderate degree of (not necessarily local)
non-Gaussianity induces a significant skewness (~ 0.1-0.2) in the relative
velocity distribution, making it a potentially interesting probe of
non-Gaussianity on intermediate to large scales. We also study two-point
correlations in redshift-space. The well-known Kaiser formula is still a good
approximation on large scales, if the Gaussian halo bias is replaced with its
(scale-dependent) non-Gaussian generalization. However, there are additional
terms not encompassed by this simple formula which become relevant on smaller
scales (k >~ 0.01 h/Mpc). Depending on the allowed level of non-Gaussianity,
these could be of relevance for future large spectroscopic surveys.
