Knowledge of water-surface velocities in rivers is useful for understanding a range of river processes. In cold regions, river-ice break up and the related downstream transport of ice debris is often the most important hydrological event of the year, leading to flood levels that typically exceed those for the open-water period and to strong consequences for river infrastructure and ecology. Accurate and complete surface-velocity fields on rivers have rarely been produced. Here, we track river ice debris over a time period of about one minute, which is the typical time lag between the two or more images that form a stereo data set in spaceborne, along-track optical stereo mapping. Using a series of nine stereo scenes from the US/Japanese Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) onboard the NASA Terra spacecraft with 15 m image resolution, we measure the ice and water velocity field over a 620 km-long reach of the lower Lena River, Siberia, just above its entry into the Lena delta. Careful analysis and correction of higher-order image and sensor errors enables an accuracy of ice-debris velocities of up to 0.04 m s-1 from the ASTER data. Maximum ice or water speeds, respectively, reach up to 2.5 m s-1 at the time of data acquisition, 27 May 2011 (03:30 UTC). Speeds show clear along-stream undulations with a wavelength of about 21 km that agree well with variations in channel width and with the location of sand bars along the river reach studied. The methodology and results of this study could be valuable to a number of disciplines requiring detailed information about river flow, such as hydraulics, hydrology, river ecology and natural-hazard management.