The combination of high power laser beams with microfluidic delivery of cells is at the heart of high-throughput, single-cell analysis and disease diagnosis with an optical stretcher. So far, the challenges arising from this combination have been addressed by externally aligning optical fibres with microfluidic glass capillaries, which has a limited potential for integration into lab-on-a-chip environments. Here we demonstrate the successful production and use of a monolithic glass chip for optical stretching of white blood cells, featuring microfluidic channels and optical waveguides directly written into bulk glass by femtosecond laser pulses. The performance of this novel chip is compared to the standard capillary configuration. The robustness, durability and potential for intricate flow patterns provided by this monolithic optical stretcher chip suggest its use for future diagnostic and biotechnological applications.