Although patterning hundreds or thousands of electrochemical electrodes on lab-on-a-chip devices is straightforward and cost-effective using photolithography, easily making connections between hundreds of electrodes and external amplifiers remains a bottleneck. Here we describe two electrode addressing approaches using multiple fluid compartments that can potentially reduce the number of external connections by ~100-fold. The first approach enables all compartments on the device to be filled with solution at the same time, and then each fluid compartment is sequentially electrically activated to make the measurements. The second approach achieves lower measurement noise by sequentially filling recording chambers with solution. We propose an equivalent circuit to explain measurement noise in these recording configurations and demonstrate application of the approaches to measure quantal exocytosis from individual cells. A principle advantage of using these approaches is that they reduce the fraction of the microchip area that needs to be dedicated to making external connections and therefore reduces the cost per working electrode.