The mechanism responsible for the accurate partitioning of newly replicated Escherichia coli chromosomes into daughter cells remains a mystery. In this article, we use automated cell cycle imaging to quantitatively analyse the cell cycle dynamics of the origin of replication (oriC) in hundreds of cells. We exploit the natural stochastic fluctuations of the chromosome structure to map both the spatial and temporal dependence of the motional bias segregating the chromosomes. The observed map is most consistent with force generation by an active mechanism, but one that generates much smaller forces than canonical molecular motors, including those driving eukaryotic chromosome segregation.