A dual-beam fiber laser trap, termed the optical stretcher when used to deform objects, has been combined with a capillary-based microfluidic system in order to serially trap and deform biological cells. The design allows for control over the size and position of the trap relative to the flow channel. Data is recorded using video phase contrast microscopy and is subsequently analyzed using a custom edge fitting routine. This setup has been regularly used with measuring rates of 50-100 cells/h. One such experiment is presented to compare the distribution of deformability found within a normal epithelial cell line to that of a cancerous one. In general, this microfluidic optical stretcher can be used for the characterization of cells by their viscoelastic signature. Possible applications include the cytological diagnosis of cancer and the gentle and marker-free sorting of stem cells from heterogeneous populations for therapeutic cell-based approaches in regenerative medicine.