Splicing remains an incompletely understood process. Recent findings suggest that chromatin structure participates in its regulation. Here, we analyze the RNA from subcellular fractions obtained through RNA-seq in the cell line K562. We show that in the human genome, splicing occurs predominantly during transcription. We introduce the coSI measure, based on RNA-seq reads mapping to exon junctions and borders, to assess the degree of splicing completion around internal exons. We show that, as expected, splicing is almost fully completed in cytosolic polyA+ RNA. In chromatin-associated RNA (which includes the RNA that is being transcribed), for 5.6% of exons, the removal of the surrounding introns is fully completed, compared with 0.3% of exons for which no intron-removal has occurred. The remaining exons exist as a mixture of spliced and fewer unspliced molecules, with a median coSI of 0.75. Thus, most RNAs undergo splicing while being transcribed: “co-transcriptional splicing.” Consistent with co-transcriptional spliceosome assembly and splicing, we have found significant enrichment of spliceosomal snRNAs in chromatin-associated RNA compared with other cellular RNA fractions and other nonspliceosomal snRNAs. CoSI scores decrease along the gene, pointing to a “first transcribed, first spliced” rule, yet more downstream exons carry other characteristics, favoring rapid, co-transcriptional intron removal. Exons with low coSI values, that is, in the process of being spliced, are enriched with chromatin marks, consistent with a role for chromatin in splicing during transcription. For alternative exons and long noncoding RNAs, splicing tends to occur later, and the latter might remain unspliced in some cases.