The large martian outflow channels terminating in Chryse Planitia are remnants of flooding events involving the localized discharge of millions of cubic kilometers of subsurface water, more than can be regionally stored in the crust. We use a dynamic groundwater model to demonstrate that snowpack or glaciers on the Tharsis rise, formed during periods of high obliquity when ice was stable at low latitudes, may have provided an efficient source of recharge and hydraulic head for the circum-Chryse outflow channels. Water is discharged through the outflow channels several times faster in Tharsis recharge models than in comparable South Pole recharge models.