We report for the first time a microdevice that enables the selective enrichment and culture of breast cancer stem cells using the principles of mammosphere culture. For nearly a decade, researchers have identified breast cancer stem cells within heterogeneous populations of cells by utilizing low-attachment serum-free culture conditions, which lead to the formation of spheroidal colonies (mammospheres) that are enriched for cancer stem cells. While this assay has proven to be useful for identifying cancer stem cells from a bulk population, ultimately its utility is limited by difficulties in combining the mammosphere technique with other useful cellular and molecular analyses. However, integrating the mammosphere technique into a microsystem can enable it to be combined directly with a number of functions, including cell sorting and analysis, as well as popular molecular assays. In this work, we demonstrate mammosphere culture within a polydimethylsiloxane (PDMS) microsystem. We first prove that hydrophobic PDMS surfaces are as effective as commercial low-attachment plates at selectively promoting the formation of mammospheres. We then demonstrate the culture of mammospheres as large as 0.25 mm within a PDMS microsystem. Finally, we verify that reagents can be delivered to the cell culture wells exclusively by diffusion-based transport, which is necessary because the cells are unattached. This microsystem component can be integrated with other microfluidic functions, such as cell separation, sorting, and recovery, as well as molecular assays, to enable new discoveries in the biology of cancer stem cells that are not possible today.