In S phase, duplicating and assembling the whole genome into chromatin requires upregulation of replicative histone gene expression. Here, we explored how histone chaperones control histone production in human cells to ensure a proper link with chromatin assembly. Depletion of the ASF1 chaperone specifically decreases the pool of replicative histones both at the protein and RNA levels. The decrease in their overall expression, revealed by total RNA sequencing (RNA-seq), contrasted with the increase in nascent/newly synthesized RNAs observed by 4sU-labeled RNA-seq. Further inspection of replicative histone RNAs showed a 3' end processing defect with an increase of pre-mRNAs/unprocessed transcripts likely targeted to degradation. Collectively, these data argue for a production defect of replicative histone RNAs in ASF1-depleted cells. We discuss how this regulation of replicative histone RNA metabolism by ASF1 as a "chaperone checkpoint" fine-tunes the histone dosage to avoid unbalanced situations deleterious for cell survival.