We developed an integrated microfluidic cellular processing unit (mCPU) capable of autonomously isolating single cells and performing measurements and on-the-fly analysis of cell-surface dissociation rates, followed by recovery of selected cells. We performed proof-of-concept, high-throughput single-cell experiments characterizing pMHC-TCR interactions on live CD8+ T cells. The mCPU platform analyzed TCR-pMHC dissociation rates with a throughput of 50 cells per hour and hundreds of cells per run, and we demonstrate that cells can be selected, enriched, and easily recovered from the device.