The Cenozoic collision between the Indian and Asian continents formed the Tibetan plateau, beginning about 70 million years ago. Since this time, at least 1,400 km of convergence has been accommodated by a combination of underthrusting of Indian and Asian lithosphere, crustal shortening, horizontal extrusion and lithospheric delamination. Rocks exposed in the Himalaya show evidence of crustal melting and are thought to have been exhumed by rapid erosion and climatically forced crustal flow. Magnetotelluric data can be used to image subsurface electrical resistivity, a parameter sensitive to the presence of interconnected fluids in the host rock matrix, even at low volume fractions. Here we present magnetotelluric data from the Tibetan-Himalayan orogen from 77°E to 92°E, which show that low resistivity, interpreted as a partially molten layer, is present along at least 1,000 km of the southern margin of the Tibetan plateau. The inferred low viscosity of this layer is consistent with the development of climatically forced crustal flow in Southern Tibet.