We developed an allele-specific assay for transposase-accessible chromatin with high-throughput sequencing (ATAC-seq) to genotype and profile active regulatory DNA across the genome. Using a mouse hybrid F1 system, we found that monoallelic DNA accessibility across autosomes was pervasive, developmentally programmed and composed of several patterns. Genetically determined accessibility was enriched at distal enhancers, but random monoallelically accessible (RAMA) elements were enriched at promoters and may act as gatekeepers of monoallelic mRNA expression. Allelic choice at RAMA elements was stable across cell generations and bookmarked through mitosis. RAMA elements in neural progenitor cells were biallelically accessible in embryonic stem cells but premarked with bivalent histone modifications; one allele was silenced during differentiation. Quantitative analysis indicated that allelic choice at the majority of RAMA elements is consistent with a stochastic process; however, up to 30% of RAMA elements may deviate from the expected pattern, suggesting a regulated or counting mechanism.