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The Antarctic Ice Sheet (AIS) is the largest ice sheet on Earth and hence a major potential contributor to future global sea-level rise. A wealth of studies suggest that increasing oceanic temperatures could cause a collapse of its marine-based western sector, the West Antarctic Ice Sheet, through the mechanism of marine ice-sheet instability, leading to a sea-level increase of 3-5 m. Thus, it is crucial to constrain the sensitivity of the AIS to rapid climate changes. The last glacial period is an ideal benchmark period for this purpose as it was punctuated by abrupt Dansgaard-Oeschger events at millennial timescales. Because their center of action was in the North Atlantic, where their climate impacts were largest, modeling studies have mainly focused on the millennial-scale evolution of Northern Hemisphere (NH) paleo ice sheets. Sea-level reconstructions attribute the origin of millennial-scale sea-level variations mainly to NH paleo ice sheets, with a minor but not negligible role of the AIS. Here we investigate the AIS response to millennialscale climate variability for the first time. To this end we use a three-dimensional, thermomechanical hybrid, ice sheet-shelf model. Different oceanic sensitivities are tested and the sea-level equivalent (SLE) contributions computed. We find that whereas atmospheric variability has no appreciable effect on the AIS, changes in submarine melting rates can have a strong impact on it. We show that in contrast to the widespread assumption that the AIS is a slow reactive and static ice sheet that responds at orbital timescales only, it can lead to ice discharges of around 6m SLE, involving substantial grounding line migrations at millennial timescales.