We report on laboratory experiments which simulate the breakdown of organic compounds under Martian surface conditions. Chambers containing Mars-analog soil mixed with the amino acid glycine were evacuated and filled to 100 mbar pressure with a Martian atmosphere gas mixture and then irradiated with a broad spectrum Xe lamp. Headspace gases were periodically withdrawn and analyzed via gas chromatography for the presence of organic gases expected to be decomposition products of the glycine. The quantum efficiency for the decomposition of glycine by light at wavelengths from 2000 to 2400 angstroms was measured to be 1.46 +/- 1.0 x 10(-6) molecules/photon. Scaled to Mars, this represents an organic destruction rate of 2.24 +/- 1.2 x 10(-4) g of C m-2 yr-1. We compare this degradation rate with the rate that organic compounds are brought to Mars as a result of meteoritic infall to show that organic compounds are destroyed on Mars at rates far exceeding the rate that they are deposited by meteorites. Thus the fact that no organic compounds were found on Mars by the Viking Lander Gas Chromatograph Mass Spectrometer experiment can be explained without invoking the presence of strong oxidants in the surface soils. The organic destruction rate may be considered as an upper bound for the globally averaged biomass production rate of extant organisms at the surface of Mars. This upper bound is comparable to the slow growing cryptoendolithic microbial communities found in dry Antarctica deserts. Finally, comparing these organic destruction rates to recently reported experiments on the stability of carbonate on the surface of Mars, we find that organic compounds may currently be more stable than calcite.