We identify two previously unknown subglacial lakes beneath the stagnated trunk of the Kamb Ice Stream (KIS). Rapid fill-drain hydrologic events over several months are inferred from surface height changes measured by CryoSat-2 altimetry and indicate that the lakes are probably connected by a subglacial drainage network, whose structure is inferred from the regional hydraulic potential and probably links the lakes. The sequential fill-drain behavior of the subglacial lakes and concurrent rapid thinning in a channel-like topographic feature near the grounding line implies that the subglacial water repeatedly flows from the region above the trunk to the KIS grounding line and out beneath the Ross Ice Shelf. Ice shelf elevation near the hypothesized outlet is observed to decrease slowly during the study period. Our finding supports a previously published conceptual model of the KIS shutdown stemming from a transition from distributed flow to well-drained channelized flow of subglacial water. However, a water-piracy hypothesis in which the KIS subglacial water system is being starved by drainage in adjacent ice streams is also supported by the fact that the degree of KIS trunk subglacial lake activity is relatively weaker than those of the upstream lakes.