The HUSH complex represses retroviruses, transposons and genes to maintain the integrity of vertebrate genomes. HUSH regulates deposition of the epigenetic mark H3K9me3, but how its three core subunits - TASOR, MPP8 and Periphilin - contribute to assembly and targeting of the complex remains unknown. Here, we define the biochemical basis of HUSH assembly and find that its modular architecture resembles the yeast RNA-induced transcriptional silencing complex. TASOR, the central HUSH subunit, associates with RNA processing components. TASOR is required for H3K9me3 deposition over LINE-1 repeats and repetitive exons in transcribed genes. In the context of previous studies, this suggests that an RNA intermediate is important for HUSH activity. We dissect the TASOR and MPP8 domains necessary for transgene repression. Structure-function analyses reveal TASOR bears a catalytically-inactive PARP domain necessary for targeted H3K9me3 deposition. We conclude that TASOR is a multifunctional pseudo-PARP that directs HUSH assembly and epigenetic regulation of repetitive genomic targets.