In 1975, a 514 meter-deep test well was drilled on Nantucket Island, Massachusetts, by the US Geological Survey to characterize the geology and hydrogeology of the Atlantic continental shelf. Salinity data, analyzed at the time of drilling, indicated that the coastal plain salinity patterns are far out of equilibrium with modern sea level conditions. The relatively thick clay layers within the coastal plain deposits have pore fluid salinities between 30% to 70% of seawater values whereas the aquifers are almost entirely fresh. The salinity patterns within the confining units resemble diffusional profiles. Prior studies have proposed that the low salinity levels within the coastal plain aquifers are due to 120 meter sea level oscillations during the past 2 million years associated with the waxing and waning of the Laurentide ice sheet. We have reanalyzed this data and propose that the salinity data within the deep Nantucket well is best explained by the rapid influx of sub-ice sheet glacial meltwaters under high pressures. We have tested these alternative hypotheses using analytical and numerical modeling. We believe that the salinity patterns in the confining units are best explained by a rapid flushing event about 21,000 years ago associated with the advance of the Buzzard Bay Lobe of the Laurentide Ice Sheet.