  Compact substructure is expected to arise in a starless core as mass becomes
concentrated in the central region likely to form a protostar. Additionally,
multiple peaks may form if fragmentation occurs. We present ALMA Cycle 2
observations of 60 starless and protostellar cores in the Ophiuchus molecular
cloud. We detect eight compact substructures which are >15 arcsec from the
nearest Spitzer YSO. Only one of these has strong evidence for being truly
starless after considering ancillary data, e.g., from Herschel and X-ray
telescopes. An additional extended emission structure has tentative evidence
for starlessness. The number of our detections is consistent with estimates
from a combination of synthetic observations of numerical simulations and
analytical arguments. This result suggests that a similar ALMA study in the
Chamaeleon I cloud, which detected no compact substructure in starless cores,
may be due to the peculiar evolutionary state of cores in that cloud.
