We have mapped a giant molecular cloud in the giant HII region NGC 604 in M33 in the 492 GHz ^ { 3 } P _ { 1 } \rightarrow ^ { 3 } P _ { 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 \to 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 ( \sim 0.2 ) facing the HII region and lowest ( \lesssim 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 .