A climatically-induced acceleration in ocean-driven melting of Antarctic ice shelves would have consequences for both the discharge of continental ice into the ocean and thus global sea level, and for the formation of Antarctic Bottom Water and the oceanic meridional overturning circulation. Using a novel gas-tight in-situ water sampler, noble gas samples have been collected from six locations beneath the Filchner Ice Shelf, the first such samples from beneath an Antarctic Ice shelf. Helium and neon are uniquely suited as tracers of glacial meltwater in the ocean. Basal meltwater fractions range from 3.6% near the ice shelf base to 0.5% near the sea floor, with distinct regional differences. We estimate an average basal melt rate for the Filchner-Ronne Ice Shelf of 177 ± 95 Gt/year, independently confirming previous results. We calculate that up to 2.7% of the meltwater has been refrozen, and we identify a local source of crustal helium.