We have developed a high-throughput single-cell ATAC-seq (assay for transposition of accessible chromatin) method to measure physical access to DNA in whole cells. Our approach integrates fluorescence imaging and addressable reagent deposition across a massively parallel (5184) nano-well array, yielding a nearly 20-fold improvement in throughput (up to ~1800 cells/chip, 4-5 hour on-chip processing time) and cost (~98{cents} per cell) compared to prior microfluidic implementations. We applied this method to measure regulatory variation in Peripheral Blood Mononuclear Cells (PBMCs) and show robust, de-novo clustering of single cells by hematopoietic cell type.