We have obtained the first ground-penetrating radar profiles of permafrost in the Dry Valleys of Antarctica. The area has long been thought of as a possible analog for Martian conditions. We interpret deltaic glacio-fluvial outwash, the disposition of lodgement till, and eroded out-wash previously thought to be terminal moraine from 100- and 400-MHz profiles at selected sites in McKelvey, central Wright, and lower Taylor Valleys, respectively. The relative permittivity appears to range between about 4 - 5.5 , which is consistent with the dense silty and sandy gravel, mineralogy and low ice content. Maximum depth of stratigraphy profiled was about 30 m. Weak interface reflectivity may limit interpretation of maximum penetration because absorption should be low, and scarce diffractions at depth imply weak scattering at 100 MHz. Future GPR systems in the Dry Valleys and on Mars should use colinear antennas to accommodate the rocky surfaces, and lower frequencies to search for deeper reflectors such as bedrock.