The centromere is an important genomic locus for chromosomal segregation. Although the centromere is specified by sequence-independent epigenetic mechanisms in most organisms, it is usually composed of highly repetitive sequences, which associate with heterochromatin. We have previously generated various chicken DT40 cell lines containing differently positioned neocentromeres, which do not contain repetitive sequences and do not associate with heterochromatin. In this study, we performed systematic 4C analysis using three cell lines containing differently positioned neocentromeres to identify neocentromere-associated regions at the 3D level. This analysis reveals that these neocentromeres commonly associate with specific heterochromatin-rich regions, which were distantly located from neocentromeres. In addition, we demonstrate that centromeric chromatin adopts a compact structure, and centromere clustering also occurs in vertebrate interphase nuclei. Interestingly, the occurrence of centromere–heterochromatin associations depend on CENP-H, but not CENP-C. Our analyses provide an insight into understanding the 3D architecture of the genome, including the centromeres.