  We have used the ARGUS multi-object spectrometer at the CTIO 4m Blanco
telescope to obtain 2756 radial velocity measurements for 1966 individual stars
in the globular cluster omega Centauri brighter than blue photographic
magnitude of about 16.5. Of these, 1589 stars are cluster members. A comparison
with two independent radial velocity studies, carried out by Suntzeff & Kraft
and by Mayor et al., demonstrates that the median error of our measurements is
below 2 km/s for the stars brighter than B-magnitude 15, which constitute the
bulk of the sample. The observed velocity dispersion decreases from about 15
km/s in the inner few arcmin to about 6 km/s at a radius of 25 arcmin. The
cluster shows significant rotation, with a maximum amplitude of about 6 km/s in
the radial zone between 6 and 10 arcmin. In a companion paper by van de Ven et
al., we correct these radial velocities for the perspective rotation caused by
the space motion of the cluster, and combine them with the internal proper
motions of nearly 8000 cluster members measured by van Leeuwen et al., to
construct a detailed dynamical model of omega Centauri and to measure its
distance.
