A model is presented for the gas phase chemistry of molecules containing sulfur in dense interstellar clouds. The sulfur chemistry is different from that used in previous models as a result of an extensive search of the recent literature and the availability of new laboratory data. The changes have a significant effect on the calculated abundance of sulfur compounds. The linked chemistry of sulfur and oxygen in the present model requires a severe depletion of sulfur and low fractional abundances of both O and O2 in the dense clouds. In contrast, the high abundance of SO and the low abundance of CS relative to SO in the HVS in the KL may indicate an oxygen-rich, high temperature environment compared to OMC-1. The formation of S-H bonds is slow because of the absence of radiative association between S(+) and H2. The present model underestimates the abundance of H2S unless a radiative association reaction between HS(+) and H2 is postulated.