Fluvial erosion is usually assumed to be absent on Venus, precluded by a high surface temperature of ~450 °C and supported by extensive uneroded volcanic flows. However, recent global circulation models suggest the possibility of Earth-like climatic conditions on Venus for much of its earlier history, prior to catastrophic runaway greenhouse warming. We observe that the stratigraphically oldest, geologically most complex units, tesserae, exhibit valley patterns morphologically similar to the patterns resulting from fluvial erosion on Earth. Given poor topographic resolution, we use an indirect technique to recognize valleys, based on the pattern of lava flooding of tesserae margins by adjacent plains volcanism. These observed valley patterns are attributed to primary geology, tectonic deformation, followed by fluvial erosion (and lesser wind erosion). This proposed fluvial erosion in tesserae provides support for climate models for a cool, wet climate on early Venus and could be an attractive research theme for future Venus missions.