  We present a high angular resolution map of 850 um continuum emission of the
Orion Molecular Cloud-3 (OMC 3) obtained with the Submillimeter Array (SMA);
the map is a mosaic of 85 pointings covering an approximate area of 6'.5 x 2'.0
(0.88 x 0.27 pc). We detect 12 spatially resolved continuum sources, each with
an H_2 mass between 0.3-5.7 Mo and a projected source size between 1400-8200
AU. All the detected sources are on the filamentary main ridge n_H2>10^6
cm^-3), and analysis based on the Jeans theorem suggests that they are most
likely gravitationally unstable. Comparison of multi-wavelength data sets
indicates that of the continuum sources, 6/12 (50 %) are associated with
molecular outflows, 8/12 (67 %) are associated with infrared sources, and 3/12
(25 %) are associated with ionized jets. The evolutionary status of these
sources ranges from prestellar cores to protostar phase, confirming that OMC-3
is an active region with ongoing embedded star-formation. We detect
quasi-periodical separations between the OMC-3 sources of ~17"/0.035 pc. This
spatial distribution is part of a large hierarchical structure, that also
includes fragmentation scales of GMC (~35 pc), large-scale clumps (~1.3 pc),
and small-scale clumps (~0.3 pc), suggesting that hierarchical fragmentation
operates within the Orion A molecular cloud. The fragmentation spacings are
roughly consistent with the thermal fragmentation length in large-scale clumps,
while for small-scale cores it is smaller than the local fragmentation length.
These smaller spacings observed with the SMA can be explained by either a
helical magnetic field, cloud rotation, or/and global filament collapse.
Finally, possible evidence for sequential fragmentation is suggested in the
northern part of the OMC-3 filament.
