Channels within the SSW rift zone of Ascraeus Mons, a large shield volcano forming part of the Tharsis volcanic province on Mars, have morphological features extremely similar to those of channels identified elsewhere on Mars as being due to fluvial action. The channel sources are too far from the caldera rim and have the wrong morphology for it to be plausible that the channels were eroded during pyroclastic flow eruptions, and the sinuosities are not consistent with scenarios involving lava flows. We propose that these channels were formed by meltwater generated and released, mainly by relatively slow seepage, when a sill was emplaced within or beneath an ice-rich permafrost layer. Smaller, fan-like channels coalescing into the amphitheater headwall of the wider ones are secondary features produced by further sapping of the undermined flank. The minimum dimensions required for the sill (∼13 by 13 km in lateral extent and ∼120 m thick) are calculated using the thermal exchanges between the sill and the permafrost implied by the volumes of the channel head craters. The corresponding minimum sill volume, ∼19 km3, is similar to that df many surface lava flows associated with the Tharsis shield volcanoes and is of the order expected for an intrusion resulting from an elastic inflation-deflation event in the summit magma reservoir.