  We present a fully sampled map of the inner 3.2 kpc of the nearby spiral
galaxy NGC 2403 in the CO J=1-0 line. These data emphasize the relatively small
contribution of molecular hydrogen to the cold gas content of this galaxy, and
confirm that the gas surface densities in the inner 2.8 kpc of NGC 2403 lie
below the critical surface density for star formation under the theory proposed
by Kennicutt (1989). Since star formation is occurring throughout the inner
disk, the simple dynamical model used by Kennicutt cannot be the only important
process regulating star formation in galaxies. We suggest that stochastic star
formation processes are responsible for the star formation seen in these
regions, and thus that supercritical gas densities may not be a necessary
condition for star formation in the inner regions of galactic disks.
