  We have surveyed submillimeter continuum emission from relatively quiescent
regions in the Orion molecular cloud to determine how the core mass function in
a high mass star forming region compares to the stellar initial mass function.
Such studies are important for understanding the evolution of cores to stars,
and for comparison to formation processes in high and low mass star forming
regions. We used the SHARC II camera on the Caltech Submillimeter Observatory
telescope to obtain 350 \micron data having angular resolution of about 9
arcsec, which corresponds to 0.02 pc at the distance of Orion. Our analysis
combining dust continuum and spectral line data defines a sample of 51 Orion
molecular cores with masses ranging from 0.1 \Ms to 46 \Ms and a mean mass of
9.8 \Ms, which is one order of magnitude higher than the value found in typical
low mass star forming regions, such as Taurus. The majority of these cores
cannot be supported by thermal pressure or turbulence, and are probably
supercritical.They are thus likely precursors of protostars. The core mass
function for the Orion quiescent cores can be fitted by a power law with an
index equal to -0.85$\pm$0.21. This is significantly flatter than the Salpeter
initial mass function and is also flatter than the core mass function found in
low and intermediate star forming regions. Thus, it is likely that
environmental processes play a role in shaping the stellar IMF later in the
evolution of dense cores and the formation of stars in such regions.
