CRISPR/Cas9 is an exciting new method for making precise changes in the DNA of chromosomes. In this study, we improved understanding of how the CRISPR/Cas9 system functions in mammalian cells, including stem cells. We showed that when CRISPR/Cas9 is used to cut DNA, the cut ends are often rejoined precisely. We used this information to develop a new method. In the method, we demonstrate that it is possible to fuse an introduced DNA fragment into the cut ends of DNA. The ends are then sealed up by the cell’s DNA repair machinery, resulting in precise addition of the introduced fragment of DNA. This method is a useful and efficient way to add specific fragments of DNA to chromosomes at precise locations. This ability is valuable for marking genes, manipulating gene expression, and many other uses. Therefore, this study adds new tools for creating useful modifications in mammalian cells, including stem cells.