Recent years have seen an unprecedented surge of research activity in studies of gene expression. This extensive work, however, has been almost uniformly focused on genome-wide gene expression and has largely ignored the fundamental fact that every gene has a specific chromosome location. We propose a novel method of spectral analysis for detecting hidden periodicities in gene expression signals ordered along the length of each chromosome. Using this method, we have discovered that each chromosome in rodents and humans has a unique periodic pattern of gene expression. The uncovered spatial periodicities in gene expression are tissue-specific in the sense that the largest differences in humans were observed between two normal tissues (brain and mammary gland) as well as between their tumor counterparts (glioma and breast cancer). The smallest differences resulted from the comparison of tumors (glioma and breast cancer) with their normal counterparts. All such effects do not extend to all chromosomes but are limited to only some of them. The estimated periods and amplitudes are identical for the genes located on the positive and negative DNA strands. While precise molecular mechanisms of chromosome-specific periodicities in gene expression have yet to be unraveled, their universal presence in different tissues adds another dimension to the current understanding of the genome organization.