We have mapped the W3 giant molecular cloud in the C03P1-3P0 ([C I] 492 GHz) and 12CO J=3-2 emission lines with the Mount Fuji Submillimeter-wave Telescope. The [C I] distribution is extended over the molecular cloud, having peaks at three star forming clouds, W3 Main, W3(OH), and AFGL 333. The [C I] emission is found to be strong in the AFGL 333 cloud, where the 12CO J=3-2 emission is relatively weak. In order to characterize the physical and chemical states of the AFGL 333 cloud, we have also observed the CO J=1-0 isotopomer lines and the CCS and N2H+ lines with the Nobeyama Radio Observatory 45 m Telescope. The [C0]/[CO] and [CCS]/[N2H+] abundance ratios are found to be higher in the AFGL 333 cloud than in the W3(OH) cloud, suggesting that the AFGL 333 cloud is younger than the W3(OH) cloud. In the AFGL 333 cloud we have found two massive cores without any sign of active star formation. They are highly gravitationally bound and are regarded as good candidates for a massive prestellar core.