Single-cell transcriptome analysis of 2544 human pancreas cells from donors, spanning six decades of life. Islet cells from older donors have increased levels of disorder as measured both by noise in the transcriptome and by the number of cells which display inappropriate hormone expression, revealing a transcriptional instability associated with aging. By analyzing the spectrum of somatic mutations in single cells from previously-healthy donors, we find a specific age-dependent mutational signature characterized by C to A and C to G transversions, indicators of oxidative stress, which is absent in single cells from human brain tissue or in a tumor cell line. Cells carrying a high load of such mutations also express higher levels of stress and senescence markers, including FOS, JUN, and the cytoplasmic superoxide dismutase SOD1, markers previously linked to pancreatic diseases with substantial age-dependent risk, such as type 2 diabetes mellitus and adenocarcinoma.