The Set1 family of histone H3 lysine 4 (H3K4) methyltransferases is highly conserved from yeast to human. Here we show that the Set1 complex (Set1C) directly binds RNA in vitro through the regions that comprise the double RNA recognition motifs (dRRM) and N-SET domain within Set1 and its subunit Spp1. To investigate the functional relevance of RNA binding, we performed UV RNA crosslinking (CRAC) for Set1 and RNA polymerase II in parallel with ChIP-seq experiments. Set1 binds nascent transcripts through its dRRM. RNA binding is important to define the appropriate topology of Set1C distribution along transcription units and correlates with the efficient deposition of the H3K4me3 mark. In addition, we uncovered that Set1 binds to different classes of RNAs to levels that largely exceed the levels of binding to the general population of transcripts, suggesting the Set1 persists on these RNAs after transcription. This class includes RNAs derived from SET1, Ty1 retrotransposons, specific transcription factors genes and snRNAs (small nuclear RNAs). We propose that Set1 modulates adaptive responses, as exemplified by the post-transcriptional inhibition of Ty1 retrotransposition.