New spacecraft observations in the Nili Fossae region of Mars reveal two valley networks (~80 and ~200 km long) that each formed distributary fans as they entered an ancient 40-km diameter impact crater. An outlet channel on the eastern crater rim, lying at an elevation above the fans, suggests these fans formed as subaqueous deltas in a crater lake. Water flowing in the valley networks entered the crater and deposited the fans, and ponded to a maximum depth of about 450 m. The lake then overtopped and breached the crater rim, incising it and dropping the lake level by ~100 m. Geological evidence, combined with the volume of water necessary to fill the crater, suggests the duration of flow through this system was prolonged. The existence of the deposits described here implies that the early Martian environment supported overland flow and ponding of water for an extended period of time.