Many human genes that control human embryonic development and differentiation of human cells form chromosomal contact with rRNA gene clusters, which are involved in the epigenetic regulation of many genes. The sites of rRNA gene contact often fall on extended (up to 50 kb) regions containing a chromatin mark, H3K27ac histone, typical for superenhancers, as well as on pericentromeric and subtelomeric regions of chromosomes. We found that the DUX4 genes located in the subtelomeric region of human chromosome 4 are surrounded by regions that are often in contact with the rRNA genes. The 25 kb region of this chromosome, presented in version hg19 of the sequenced human genome, contains several copies of the DUX4 gene. The sites of rRNA gene contacts located around this region contain methylation sites as well as CTCF binding sites. It is assumed that the rRNA gene contacts are important in silencing these DUX4 gene copies.