Neurons and endocrine cells secrete neurotransmitter and hormones in discrete packets in a process called quantal exocytosis. Electrochemical microelectrodes can detect spikes in current resulting from the oxidation of individual quanta of transmitter only if the electrodes are small and directly adjacent to release sites on the cell. Here we report development of a microchip device that uses microfluidic traps to automatically target individual or small groups of cells to small electrochemical electrodes. Microfluidic channels and traps were fabricated by multi-step wet etch of a silicon wafer whereas Pt electrodes were patterned in register with the trap sites. We demonstrate high-resolution amperometric measurement of quantal exocytosis of catecholamines from chromaffin cells on the device. This reusable device is a step towards developing high-throughput lab-on-a-chip instruments for recording quantal exocytosis to increase the pace of basic neuroscience research and to enable screening of drugs that target exocytosis.