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Distributed Acoustic Sensing (DAS) is a new technology in which seismic energy is detected, at high spatial and temporal resolution, using the propagation of laser pulses in a fiber‐optic cable. We show analyses from the first glaciological borehole DAS deployment to measure the englacial and subglacial seismic properties of Store Glacier, a fast‐flowing outlet of the Greenland Ice Sheet. We record compressional and shear waves in 1,043 m‐deep vertical seismic profiles, sampled at 10 m vertical resolution, and detect a transition from isotropic to anisotropic ice at 84% of ice thickness, consistent with the Holocene‐Wisconsin transition. We identify subglacial reflections originating from the base of a 20 m‐thick layer of consolidated sediment and, from attenuation measurements, interpret temperate ice in the lowermost 100 m of the glacier. Our findings highlight the promising potential of DAS technology to constrain the seismic properties of glaciers and ice sheets. Plain Language Summary: Distributed Acoustic Sensing (DAS) is a new technology for seismic surveying in which the transmission of light through fiber‐optic cables is used to record seismic energy, with unprecedented spatial resolution compared to traditional techniques. Our paper presents data from the first borehole‐glaciological deployment of DAS, in which fiber‐optic cable was installed in a 1,043 m‐deep vertical borehole on Store Glacier, a fast‐flowing outlet of the Greenland Ice Sheet. The detailed seismic anatomy of the glacier that our survey provides—an independent measurement of the seismic response every 10 m—gives new insights about its internal flow regime and temperature and even allows us to detect layers of sediment underlying it. We predict that DAS surveying will play an increasingly large role in future glaciological investigations as the recognition of its promising potential grows. Key Points: Distributed Acoustic Sensing (DAS) is a new technology for recording seismic data using laser pulses propagating in a fiber‐optic cableWe present the first borehole‐glaciological application of DAS, installing cable in a 1,043 m‐deep borehole on Greenland's Store GlacierWe evidence, at 10 m vertical resolution, anisotropic and temperate ice beyond ~880 m depth and ~20 m of consolidated subglacial sediment [ABSTRACT FROM AUTHOR]