Sister chromatids, the products of eukaryotic DNA replication, are held together by the chromosomal cohesin complex after their synthesis. This allows the spindle in mitosis to recognize pairs of replication products for segregation into opposite directions. Cohesin forms large protein rings that may bind DNA strands by encircling them, but the characterization of cohesin binding to chromosomes in vivo has remained vague. We have performed high resolution analysis of cohesin association along budding yeast chromosomes III-VI. Cohesin localizes almost exclusively between genes that are transcribed in converging directions. We find that active transcription positions cohesin at these sites, not the underlying DNA sequence. Cohesin is initially loaded onto chromosomes at separate places, marked by the Scc2/Scc4 cohesin loading complex, from where it appears to slide to its more permanent locations. But even after sister chromatid cohesion is established, changes in transcription lead to repositioning of cohesin. Thus the sites of cohesin binding and therefore probably sister chromatid cohesion, a key architectural feature of mitotic chromosomes, display surprising flexibility. Cohesin localization to places of convergent transcription is conserved in fission yeast, suggesting that it is a common feature of eukaryotic chromosomes.