  Observed HI accretion around nearby galaxies can only account for a fraction
of the gas supply needed to sustain the currently observed star formation
rates. It is possible that additional accretion happens in the form of low
column density cold flows, as predicted by numerical simulations of galaxy
formation. To contrain the presence and properties of such flows, we present
deep HI observations obtained with the NRAO Green Bank Telescope of an area
measuring 4 by 4 degrees around NGC 2403. These observations, with a 5 sigma
detection limit of 2.4 x 10^18 cm^-2 over a 20 km/s linewidth, reveal the
presence of a low-column density, extended cloud outside the main HI disk,
about 17' (~16 kpc or ~2R25) to the NW of the center of the galaxy. The total
HI mass of the cloud is 6.3 x 10^6 Msun, or 0.15 percent of the total HI mass
of NGC 2403. The cloud is associated with an 8-kpc anomalous-velocity HI
filament in the inner disk, previously observed in deep VLA observations by
Fraternali et al. (2001, 2002). We discuss several scenarios for the origin of
the cloud, and conclude that it is either accreting from the intergalactic
medium, or is the result of a minor interaction with a neigbouring dwarf
galaxy.
