Many investigators of the early martian climate have suggested that a dense carbon dioxide atmosphere was present and warmed the surface above the melting point of water (J.B. Pollack, J.F. Kasting, S.M. Richardson, and K. Poliakoff 1987. Icarus 71, 203-224). However, J.F. Kasting (1991. Icarus 94, 1-13) pointed out that previous thermal models of the primitive martian atmosphere had not considered the condensation of CO2. When this effect was incorporated, Kasting found that CO2 by itself is inadequate to warm the surface. SO2 absorbs strongly in the near UV region of the solar spectrum. While a small amount of SO2 may have a negligible effect by itself on the surface temperature, it may have significantly warmed the middle atmosphere of early Mars, much as ozone warms the terrestrial stratosphere today. If this region is kept warm enough to inhibit the condensation of CO2, then CO2 remains a viable greenhouse gas. Our preliminary radiative modeling shows that the addition of 0.1 ppmv of SO2 in a 2 bar CO2 atmosphere raises the temperature of the middle atmosphere by approximately 10 degrees, so that the upper atmosphere in a 1 D model remains above the condensation temperature of CO2. In addition, this amount of SO2 in the atmosphere provides an effective UV shield for a hypothetical biosphere on the martian surface.