Cell types can be classified according to shared patterns of transcription. Non-genetic variability among individual cells of the same type has been ascribed to stochastic transcriptional bursting and transient cell states. Using high-coverage single-cell RNA profiling, we asked whether long-term, heritable differences in gene expression can impart diversity within cells of the same type. Studying clonal human lymphocytes and mouse brain cells, we uncovered a vast diversity of heritable gene expression patterns among different clones of cells of the same type in vivo. We combined chromatin accessibility and RNA profiling on different lymphocyte clones to reveal thousands of regulatory regions exhibiting interclonal variation, which could be directly linked to interclonal variation in gene expression. Our findings identify a source of cellular diversity, which may have important implications for how cellular populations are shaped by selective processes in development, aging, and disease. A record of this paper's transparent peer review process is included in the supplemental information.