We have mapped a giant molecular cloud in the giant HII region NGC 604 in M33
in the 492 GHz ^3P_1 -- ^3P_0 transition of neutral atomic carbon using the
James Clerk Maxwell Telescope. We find the distribution of the [CI] emission to
be asymmetric with respect to the CO J=1--0 emission, with the peak of the [CI]
emission offset towards the direction of the center of the HII region. In
addition, the line ratio I_{[CI]}/I_{CO} is highest (~ 0.2) facing the HII
region and lowest (< 0.1) away from it. These asymmetries indicate an edge-on
morphology where the [CI] emission is strongest on the side of the cloud facing
the center of the HII region, and not detected at all on the opposite side This
suggests that the sources of the incident flux creating C from the dissociation
of CO are the massive stars of the HII region. The lowest line ratios are
similar to what is observed in Galactic molecular clouds, while the highest are
similar to starburst galaxies and other regions of intense star formation. The
column density ratio, N(C)/N(H_2) is a few times 10^{-6}, in general agreement
with models of photodissociation regions.Comment: Accepted for publication in ApJ. 8 pages, 5 figures, 3 table