Meters of DNA wrap around histone proteins to form nucleosomes and fit inside the micron-diameter nucleus. For the genetic information encoded in the DNA to become available for transcription, replication and repair, the DNA--histone assembly must be disrupted. Experiment has indicated that the outer stretches of nucleosomal DNA "breathe" by spontaneously detaching from and reattaching to the histone core. Here, we report direct observation of spontaneous DNA breathing in atomistic molecular dynamics simulations, detailing a microscopic mechanism of the DNA breathing process. According to our simulations, the outer stretches of nucleosomal DNA detach in discrete steps involving five or ten base pairs, with the detachment process being orchestrated by the motion of several conserved histone residues. The inner stretches of nucleosomal DNA are found to be more stably associated with the histone core by more abundant nonspecific DNA--protein contacts, providing a microscopic interpretation of nucleosome unraveling experiments. The CG content of nucleosomal DNA is found to anticorrelate with the extent of unwrapping, supporting the possibility that AT-rich segments may signal the start of transcription by forming less stable nucleosomes.