At high altitudes (>1000 m) throughout the Dry Valleys, Antarctica, liquid water is rare, yet ground ice, which may be millions of years old, is pervasive in glacial sediments and bedrock. The origin of this ice is different from its arctic and alpine counterparts and may be similar to water on Mars. We present chemical and isotopic analyses of Antarctic ground ice from cores of Sirius Group sediments at Table Mountain in the Dry Valleys. These data, together with the presence of diagenetic calcite and chabazite in the frozen sediments, indicate that the ice and minerals accumulated over long periods of time from atmospheric water vapor and brine films formed on the surface of the ground. This analogy indicates that ferric-bearing minerals could precipitate under present conditions in the Martian soil.