A large number of measurements of nucleosome repeat lengths are analyzed and are found to exhibit preferential quantization to a set of values related by integral multiples of the helical twist of DNA. This implies that the nucleosomal DNA content is preferentially quantized, which in turn implies that linker DNA lengths are preferentially quantized. This study confirms and extends previous observations in the literature that had suggested, but not firmly established, that linker lengths might be quantized. The quantization of repeat lengths applies even for very long repeat lengths. This suggests a model for the origin of the quantization, in which the quantization arises from the requirements of higher-order chromatin structure.