  Using the Submillimeter Array (SMA), we have imaged the 1.3 millimeter
continuum emission at the center of the massive star-forming regions NGC 6334 I
and I(N). In both regions, the SMA observations resolve the emission into
multiple millimeter sources, with most of the sources clustered into areas only
10,000 AU in diameter. Toward NGC 6334 I, we find four compact sources: the two
brightest (I-SMA1 and I-SMA2) are associated with previously-known ammonia
cores; I-SMA3 is coincident with the peak of the compact HII region (NGC 6334
F); and I-SMA4 is a newly-discovered object. While I-SMA3 exhibits a mixture of
free-free and dust emission, the rest of the objects are dust cores. Toward NGC
6334 I(N), seven compact dust cores are found, one of which is associated with
a faint centimeter source. With the exception of I-SMA3, none of the millimeter
sources have infrared counterparts in Spitzer Space Telescope 3-8 micron
images. Using a simple physical model for the dust continuum emission, the
estimated mass of interstellar material toward each of these compact objects is
in the range of 3 to 66 solar masses. The total mass in the compact objects
appears to be similar in I and I(N). The small size of these groups of sources
suggest that these objects are proto-Trapezia forming in the centers of
clusters of low to intermediate-mass stars.
