Measuring chromatin accessibility is a powerful method to identify cell types and states. Performed at single-cell resolution, this assay has generated catalogs of genome-wide DNA regulatory sites, whole-organism cell atlases, and dynamic chromatin reorganization through development. However, the limited throughput of current single-cell approaches poses a challenge for implementing proper study designs, population-scale profiling, and/or very deep profiling of complex samples. To this end, we developed a 10X-compatible combinatorial indexing ATAC sequencing ("txci-ATAC-seq"), which is a combinatorial indexing framework that initially indexes ("pre-indexes") chromatin within nuclei with barcoded transposases followed by encapsulation and further barcoding using a commercialized droplet-based microfluidics platform (10X Genomics). Leveraging this molecular hashing strategy, we demonstrate that txci-ATAC-seq enables the indexing of up to 200,000 nuclei across multiple samples in a single emulsion reaction, representing a ~22-fold increase in throughput compared to the standard workflow at the same collision rate. To improve the efficiency of this new technique, we further developed a faster version of the protocol ("Fast-txci-ATAC-seq") that separates sample pre-processing from library generation and has the potential to profile up to 96 samples simultaneously. We initially benchmarked our assay by generating chromatin accessibility profiles for 230,018 cells from five native tissues across three experiments, including human cortex (28,513 cells), mouse brain (48,997 cells), human lung (15,799 cells), mouse lung (73,280 cells), and mouse liver (63,429 cells). We also applied our method to a club cell secretory protein knockout (CC16-/-) mouse model to examine the biological and technical limitations of the mouse line. By characterizing DNA regulatory landscapes in 76,498 wild-type and 77,638 CC16-/-murine lung nuclei, our investigations uncovered previously unappreciated residual genetic deviations from the reference strain that resulted from the method of gene targeting, which employed embryonic stem cells from the 129 strain. We found that these genetic remnants from the 129 strain led to profound cell-type-specific changes in chromatin accessibility in regulatory elements near a host of genes. Collectively, we defined single-cell chromatin signatures in 384,154 nuclei from 13 primary samples across different species, organs, biological replicates, and genetic backgrounds, establishing txci-ATAC-seq as a robust, high-quality, and highly multiplexable single-cell assay for large-scale chromatin studies.