DNA wrapped in nucleosomes is sterically occluded, creating obstacles for proteins that must bind it. How proteins gain access to DNA buried inside nucleosomes is not known. Here we report measurements of the rates of spontaneous nucleosome conformational changes in which a stretch of DNA transiently unwraps off the histone surface, starting from one end of the nucleosome, and then rewraps. The rates are rapid. Nucleosomal DNA remains fully wrapped for only approximately 250 ms before spontaneously unwrapping; unwrapped DNA rewraps within approximately 10-50 ms. Spontaneous unwrapping of nucleosomal DNA allows any protein rapid access even to buried stretches of the DNA. Our results explain how remodeling factors can be recruited to particular nucleosomes on a biologically relevant timescale, and they imply that the major impediment to entry of RNA polymerase into a nucleosome is rewrapping of nucleosomal DNA, not unwrapping.