Non-coding Y RNAs are essential for the initiation of chromosomal DNA replication in vertebrates, yet their association with chromatin during the cell cycle is not characterised. Here, we quantify human Y RNA levels in soluble and chromatin-associated intracellular fractions and investigate, topographically, their dynamic association with chromatin during the cell cycle. We find that, on average, about a million Y RNA molecules are present in the soluble fraction of a proliferating cell, and 5-10-fold less are in association with chromatin. These levels decrease substantially during quiescence. No significant differences are apparent between cancer and non-cancer cell lines. Y RNAs associate with euchromatin throughout the cell cycle. Their levels are 2-4-fold higher in S phase than in G1 phase or mitosis. Y RNAs are not detectable at active DNA replication foci, and re-associate with replicated euchromatin during mid and late S phase. The dynamics and sites of Y1 RNA association with chromatin are in concordance with those of the origin recognition complex (ORC). Our data therefore suggest a functional role of Y RNAs in a common pathway with ORC.