  To study the evolution of high mass cores, we have searched for evidence of
collapse motions in a large sample of starless cores in the Orion molecular
cloud. We used the Caltech Submillimeter Observatory telescope to obtain
spectra of the optically thin (\H13CO+) and optically thick (\HCO+) high
density tracer molecules in 27 cores with masses $>$ 1 \Ms. The red- and
blue-asymmetries seen in the line profiles of the optically thick line with
respect to the optically thin line indicate that 2/3 of these cores are not
static. We detect evidence for infall (inward motions) in 9 cores and outward
motions for 10 cores, suggesting a dichotomy in the kinematic state of the
non-static cores in this sample. Our results provide an important observational
constraint on the fraction of collapsing (inward motions) versus non-collapsing
(re-expanding) cores for comparison with model simulations.
