In fission yeast and plants, RNA processing and degradation contribute to heterochromatin silencing, alongside conserved pathways of transcriptional repression. It has not been known whether similar pathways exist in metazoans. Here, we describe a pathway of silencing in Caenorhabditis elegans somatic cells, in which the highly conserved RNA-binding complex LSM2-8 contributes selectively to the repression of heterochromatic reporters and endogenous genes bearing the Polycomb mark, histone H3K27me3. This acts by degrading selected transcripts through the XRN-2 exoribonuclease. Disruption of the LSM2-8 pathway leads to mRNA stabilization. Unlike previously described pathways of heterochromatic RNA degradation, LSM2-8-mediated RNA degradation does not target nor require H3K9 methylation. Intriguingly, loss of this pathway coincides with a localized reduction in H3K27me3 at lsm-8-sensitive loci. We have thus uncovered a mechanism of RNA degradation that selectively contributes to the silencing of a subset of H3K27me3-marked genes, revealing a previously unrecognized layer of post-transcriptional control in metazoan heterochromatin.