Kasei Valles compose an enormous outflow-channel system on Mars. The upper part of the channel system is typically less than 1 km deep and descends from Echus Chasma about 1 km over a distance of 1000 km; it then splits into north and south channels. On the basis of a stereomodel of Viking images, we have measured the geometry of a steep, constricted reach of the north channel that drops 900 m in only 100 km. A late-stage flood is hypothesized to have scoured the channel. If we assume that channel striations indicate water levels, then the flood had a minimum cross-sectional area of 3.12 x 107 m2 (the putative flood had a width of 83 km, an average depth of 374 m, and maximum depth of 1280 m). These channel measurements suggest that flood velocities ranged from 32 to 75 m⋅s-1 and that discharge was greater than 1 km3⋅s-1, values larger than those calculated for any other flood event on Mars or Earth. The flood maintained supercritical flow and caused intense erosion in this area, scouring a 350-m-deep megapothole. The source of the flood water may have been a temporary lake in Echus Chasma, a deep canyon formed in association with tectonism at Valles Marineris.