  We used the NRAO Very Large Array to search for 3.6 cm continuum emission
from embedded protostars in a sample of 8 nearby ``starless'' cores that show
spectroscopic evidence for infalling motions in molecular emission lines. We
detect a total of 13 compact sources in the eight observed fields to 5 sigma
limiting flux levels of typically 0.09 mJy. None of these sources lie within 1'
of the central positions of the cores, and they are all likely background
objects. Based on an extrapolation of the empirical correlation between the
bolometric luminosity and 3.6 cm luminosity for the youngest protostars, these
null-detections place upper limits of ~0.1 L_sun (d/140pc)^2 on the
luminosities of protostellar sources embedded within these cores. These limits,
together with the extended nature of the inward motions inferred from molecular
line mapping (Lee et al. 2001), are inconsistent with the inside-out collapse
model of singular isothermal spheres and suggest a less centrally condensed
phase of core evolution during the earliest stages of star formation.
