Protein Arginine Methyltransferase 5 (PRMT5) regulates RNA splicing and transcription by symmetric dimethylation of arginine residues (Rme2s/SDMA) in many RNA binding proteins. However, the mechanism by which PRMT5 couples splicing to transcriptional output is unknown. Here, we demonstrate that a major function of PRMT5 activity is to promote chromatin escape of a novel, large class of mRNAs that we term Genomically Retained Incompletely Processed Polyadenylated Transcripts (GRIPPs). Using nascent and total transcriptomics, spike-in controlled fractionated cell transcriptomics, and total and fractionated cell proteomics, we show that PRMT5 inhibition and knockdown of the PRMT5 SNRP (Sm protein) adapter protein pICln (CLNS1A) -but not type I PRMT inhibition-leads to gross detention of mRNA, SNRPB, and SNRPD3 proteins on chromatin. Compared to most transcripts, these chromatin-trapped polyadenylated RNA transcripts have more introns, are spliced slower, and are enriched in detained introns. Using a combination of PRMT5 inhibition and inducible isogenic wildtype and arginine-mutant SNRPB, we show that arginine methylation of these snRNPs is critical for mediating their homeostatic chromatin and RNA interactions. Overall, we conclude that a major role for PRMT5 is in controlling transcript processing and splicing completion to promote chromatin escape and subsequent nuclear export.