The Brahmaputra River slices an exceptionally deep canyon through the eastern Himalaya. Fission-track and laser-ablation U-Pb ages of detrital zircon grains from the river document very rapid erosion from this region and its impact on sediment fluxes downstream in the Brahmaputra. Downstream from the canyon, 47% of the detrital zircons in the river's modern sediment load comprise a fission-track age population averaging only 0.6 Ma. Equally young cooling ages are reported from bedrock in the canyon through the Namche Barwa–Gyala Peri massif but are absent from riverbank sands of major tributaries upstream. Simple mixing models of U-Pb ages on detrital zircons from samples taken above and below this massif independently suggest that 45% of the downstream detrital zircons are derived from the basement gneisses extensively exposed in the massif. Constraints on the extent of the source area provided by bedrock cooling ages together with sediment-flux estimates at Pasighat, India, suggest exhumation rates averaging 7–21 mm yr−1 in an area of ~3300 km2 centered on the massif. This rapid exhumation, which is consistent with the very young cooling ages of the detrital zircons from this area, produces so much sediment that ~50% of the vast accumulation in the Brahmaputra system at the front of the Himalaya comes from only ~2% of its drainage. This extreme localization of rapid erosion, sediment evacuation, and bedrock cooling bear on (1) common assumptions in geodynamic and geochemical studies of the Himalaya about sources of sediment, and (2) plans for hydroelectric development and flood management in southeastern Tibet and the heavily populated areas of eastern India.