Faithful DNA replication ensures genetic integrity in eukaryotic cells, but it is still obscure how replication is organized in space and time within the nucleus. Using timelapse microscopy, we have developed a new assay to analyze the dynamics of DNA replication both spatially and temporally in individual Saccharomyces cerevisiae cells. This allowed us to visualize replication factories, nuclear foci consisting of replication proteins where the bulk of DNA synthesis occurs. We show that the formation of replication factories is a consequence of DNA replication itself. Our analyses of replication at specific DNA sequences support a long-standing hypothesis that sister replication forks generated from the same origin stay associated with each other within a replication factory while the entire replicon is replicated. This assay system allows replication to be studied at extremely high temporal resolution in individual cells, thereby opening a window into how replication dynamics vary from cell to cell.