Long noncoding RNAs (lncRNAs) play a conserved role in regulating gene expression, chromatin dynamics, and cell differentiation. They serve as a platform for RNA interference (RNAi)-mediated heterochromatin formation or DNA methylation in many eukaryotic organisms. We found in  Schizosaccharomyces pombe  that heterochromatin is lost at transcribed regions in the absence of RNA degradation. We show that heterochromatic RNAs are retained on chromatin, form DNA:RNA hybrids, and need to be degraded by the Ccr4-Not complex or RNAi to maintain heterochromatic silencing. The Ccr4-Not complex is localized to chromatin independently of H3K9me and degrades chromatin-associated transcripts, which is required for transcriptional silencing. Overexpression of heterochromatic RNA, but not euchromatic RNA, leads to chromatin localization and loss of silencing of a distant  ade6  reporter in wild-type cells. Our results demonstrate that chromatin-bound RNAs disrupt heterochromatin organization and need to be degraded in a process of heterochromatin formation.