Here we present advancements in single-cell combinatorial indexed ATAC-seq (sciATAC) to measure chromatin accessibility that leverage nanowell chips to achieve atlas-scale cell throughput (>105) at low cost. The platform leverages the core of the sciATAC workflow where multiple indexed tagmentation reactions are performed, followed by pooling and distribution to a second set of reaction wells for PCR-based indexing. In this work, we instead leverage a chip containing 5,184 nanowells as the PCR stage of indexing, enabling a 52-fold improvement in scale and reduction in per-cell preparation costs. We detail three variants that balance cell throughput and depth of coverage and apply these methods to banked mouse brain tissue, producing maps of cell types as well as neuronal subtypes that includes integration with exiting scATAC and scRNA-seq datasets. Our optimized workflow achieves a high fraction of reads that fall within called peaks (>80%) and low cell doublet rates. The high cell coverage technique produces high unique reads per cell, while retaining high enrichment for open chromatin regions, enabling the assessment of >70,000 unique accessible on average for each cell profiled. When compared to current methods in the field, our technique provides similar or superior per-cell information with very low levels of cell-to-cell crosstalk, and achieves this at a cost point much lower than existing assays.