One goal of regenerative medicine, to use stem cells to replace cells lost by injury or disease, depends on producing an excess of the relevant cell for study or transplantation. To this end, the stepwise differentiation of stem cells into specialized derivatives has been successful for some cell types, but a major problem remains the inefficient conversion of cells from one stage of differentiation to the next. If specialized cells are to be produced in large numbers it will be necessary to expand progenitor cells, without differentiation, at some steps of the process. Using the pancreatic lineage as a model for embryonic-stem-cell differentiation, we demonstrate that this is a solvable problem. Co-culture with organ-matched mesenchyme permits proliferation and self-renewal of progenitors, without differentiation, and enables an expansion of more than a million-fold for human endodermal cells with full retention of their developmental potential. This effect is specific both to the mesenchymal cell and to the progenitor being amplified. Progenitors that have been serially expanded on mesenchyme give rise to glucose-sensing, insulin-secreting cells when transplanted in vivo. Theoretically, the identification of stage-specific renewal signals can be incorporated into any scheme for the efficient production of large numbers of differentiated cells from stem cells and may therefore have wide application in regenerative biology.