Heterochromatic domains containing histone H3 lysine 9 methylation (H3K9me) can be epigenetically inherited independently of underlying DNA sequence. To gain insight into the mechanisms that mediate epigenetic inheritance, we used a  Schizosaccharomyces pombe  inducible heterochromatin formation system to perform a genetic screen for mutations that abolish heterochromatin inheritance without affecting its establishment. We identified mutations in several pathways, including the conserved and essential Rix1-associated complex (henceforth the rixosome), which contains RNA endonuclease and polynucleotide kinase activities with known roles in ribosomal RNA processing. We show that the rixosome is required for spreading and epigenetic inheritance of heterochromatin in fission yeast. Viable rixosome mutations that disrupt its association with Swi6/HP1 fail to localize to heterochromatin, lead to accumulation of heterochromatic RNAs, and block spreading of H3K9me and silencing into actively transcribed regions. These findings reveal a new pathway for degradation of heterochromatic RNAs with essential roles in heterochromatin spreading and inheritance.