The eukaryotic genome is packaged together with histone proteins into chromatin following DNA replication. Recent studies have shown that histones can also be assembled into chromatin independently of DNA replication and that this dynamic exchange of histones may be biased toward sites undergoing transcription. Here we show that epitope-tagged histone H4 can be incorporated into nucleosomes throughout the budding yeast (Saccharomyces cerevisiae) genome regardless of the phase of the cell cycle, the transcriptional status, or silencing of the region. Direct comparisons reveal that the amount of histone incorporation that occurs in G(1)-arrested cells is similar to that occurring in cells undergoing DNA replication. Additionally, we show that this histone incorporation is not dependent on the histone H3/H4 chaperones CAF-1, Asf1, and Hir1 individually. This study demonstrates that DNA replication and transcription are not necessary prerequisites for histone exchange in budding yeast, indicating that chromatin is more dynamic than previously thought.