In S phase, duplication and assembly of the whole genome into chromatin requires upregulation of replicative histone gene expression. Here, we explored a potential role of histone chaperones in this process thereby linking chromatin assembly with histone production in human cells. Depletion of the ASF1 chaperone specifically decreased the pool of replicative histones both at the levels of soluble protein and total RNA, while depletion of CAF-1 did not. Most replicative histone genes decreased in their overall expression as revealed by total RNA-seq. In contrast, both their newly synthesized RNAs and nascent RNAs at transcription sites increased as shown by 4sU-labeled RNA-seq and single-molecule RNA FISH, respectively. Further inspection of the sequences corresponding to replicative histone RNAs showed a 3’ processing defect, leading to unprocessed transcripts usually targeted for degradation. We discuss how this regulation of replicative histone RNA metabolism by ASF1 fine-tunes the histone dosage to avoid unbalanced situations deleterious for cell survival.