The Geostationary Imaging Fourier Transform Spectrometer (GIFTS), as part of NASA's New Millennium Program, is an advanced instrument to provide high-temporal-resolution measurements of atmospheric temperature and water vapor, which will greatly facilitate the detection of rapid atmospheric changes associated with destructive weather events, including tornadoes, severe thunderstorms, flash floods, and hurricanes. The Committee on Earth Science and Applications from Space under the National Academy of Sciences recommended that NASA and NOAA complete the fabrication, testing, and space qualification of the GIFTS instrument and that they support the international effort to launch GIFTS by 2008. Lossless data compression is critical for the overall success of the GIFTS experiment, or any other very high data rate experiment where the data is to be disseminated to the user community in real-time and archived for scientific studies and climate assessment. In general, lossless data compression is needed for high data rate hyperspectral sounding instruments such as GIFTS for (1) transmitting the data down to the ground within the bandwidth capabilities of the satellite transmitter and ground station receiving system, (2) compressing the data at the ground station for distribution to the user community (as is traditionally performed with GOES data via satellite rebroadcast), and (3) archival of the data without loss of any information content so that it can be used in scientific studies and climate assessment for many years after the date of the measurements. In this paper we study lossless compression of GIFTS data that has been collected as part of the calibration or ground based tests that were conducted in 2006. The predictive partitioned vector quantization (PPVQ) is investigated for higher lossless compression performance. PPVQ consists of linear prediction, channel partitioning and vector quantization. It yields an average compression ratio of 4.65 on the GIFTS test data, which significantly outperforms the standard compression methods such as JPEG-2000, JPEG-LS, and CCSDS IDC 9/7M & 5/3.