Following DNA replication, equal amounts of chromatin proteins are distributed over sister chromatids by re-deposition of parental chromatin proteins and deposition of newly synthesized chromatin proteins. Molecular mechanisms balancing the allocation of new and old chromatin proteins remain largely unknown. Here, we studied the genome-wide distribution of new chromatin proteins relative to parental DNA template strands and replication initiation zones using the double-click-seq. Under control conditions, new chromatin proteins were preferentially found on DNA replicated by the lagging strand machinery. Strikingly, replication stress induced by hydroxyurea or curaxin treatment and inhibition of ataxia telangiectasia and Rad3-related protein (ATR) or p53 inactivation inverted the observed chromatin protein deposition bias to the strand replicated by the leading strand polymerase in line with previously reported effects on replication protein A occupancy. We propose that asymmetric deposition of newly synthesized chromatin proteins onto sister chromatids reflects differences in the processivity of leading and lagging strand synthesis.