Two surface samples collected from the Chryse Planitia region of Mars were heated to temperatures up to 500??C, and the volatiles that they evolved were analyzed with a gas chromatograph-mass spectrometer. Only water and carbon dioxide were detected. This implies that organic compounds have not accumulated to the extent that individual components could be detected at levels of a few parts in 109 by weight in our samples. Proposed mechanisms for the accumulation and destruction of organic compounds are discussed in the light of this limit.