Rock varnish is a ubiquitous coating, usually less than 100mm thick on stable natural and cultural rock surfaces, containing small amounts of organic matter, typically less than 1% by weight. Depending on the thickness, 1,500 to 20,000 cm² of varnish is needed for tandem accelerator mass spectrometry (TAMS). The first accelerator radiocarbon dates of rock varnishes are reported here along with potassium/argon ages of lava flows and conventional radiocarbon dates of pluvial lake shorelines, which were used to provide a calibration. Cation-ratio dates were determined for 167 artifacts from the Mojave Desert, eastern California; they suggest human occupation in the late Pleistocene. -- AATA