Firre encodes a lncRNA involved in nuclear organization. Here, we show that Firre RNA expressed from the active X chromosome maintains histone H3K27me3 enrichment on the inactive X chromosome (Xi) in somatic cells. This trans-acting effect involves SUZ12, reflecting interactions between Firre RNA and components of the Polycomb repressive complexes. Without Firre RNA, H3K27me3 decreases on the Xi and the Xi-perinucleolar location is disrupted, possibly due to decreased CTCF binding on the Xi. We also observe widespread gene dysregulation, but not on the Xi. These effects are measurably rescued by ectopic expression of mouse or human Firre/FIRRE transgenes, supporting conserved trans-acting roles. We also find that the compact 3D structure of the Xi partly depends on the Firre locus and its RNA. In common lymphoid progenitors and T-cells Firre exerts a cis-acting effect on maintenance of H3K27me3 in a 26 Mb region around the locus, demonstrating cell type-specific trans- and cis-acting roles of this lncRNA.