Human herpesvirus -6A and 6B (HHV-6A/B) can integrate their genomes into the telomeres of human chromosomes. Viral integration can occur in several cell types, including germinal cells, resulting in individuals that harbor the viral genome in every cell of their body. The integrated genome is efficiently silenced but can sporadically reactivate resulting in various clinical symptoms. To date, the integration mechanism and the subsequent silencing of HHV-6A/B genes remains poorly understood. Here we investigate the genome-wide chromatin contacts of the integrated HHV-6A in latently-infected cells. We show that HHV-6A becomes transcriptionally silent upon infection of these cells over the course of seven days. In addition, we established an HHV-6-specific 4C-seq approach, revealing that the HHV-6A 3D interactome is associated with quiescent chromatin states in cells harboring integrated virus. Furthermore, we observed that the majority of virus chromatin interactions occur toward the distal ends of specific human chromosomes. Exploiting this finding, we established a 4C-seq method that accurately detects the chromosomal integration sites. We further implement long-read minION sequencing in the 4C-seq assay and developed a method to identify HHV-6A/B integration sites in clinical samples.