Three-dimensional topology of DNA in the cell nucleus provides a level of transcription regulation beyond the sequence of the linear DNA. To study the relationship between the transcriptional activity and the spatial environment of a gene, we used allele-specific chromosome conformation capture-on-chip (4C) technology to produce high-resolution topology maps of the active and inactive X chromosomes in female cells. We found that loci on the active X form multiple long-range interactions, with spatial segregation of active and inactive chromatin. On the inactive X, silenced loci lack preferred interactions, suggesting a unique random organization inside the inactive territory. However, escapees, among which is Xist, are engaged in long-range contacts with each other, enabling identification of novel escapees. Deletion of Xist results in partial refolding of the inactive X into a conformation resembling the active X without affecting gene silencing or DNA methylation. Our data point to a role for Xist RNA in shaping the conformation of the inactive X chromosome at least partially independent of transcription.