Non-coding Y RNAs are required for the initiation of chromosomal DNA replication in mammalian cells. It is unknown how they perform this function or if they associate with a nuclear structure during DNA replication. Here, we investigate the association of Y RNAs with chromatin and their interaction with replication proteins during DNA replication in a human cell-free system. Our results show that fluorescently labelled Y RNAs associate with unreplicated euchromatin in late G1 phase cell nuclei before the initiation of DNA replication. Following initiation, Y RNAs are displaced locally from nascent and replicated DNA present in replication foci. In intact human cells, a substantial fraction of endogenous Y RNAs are associated with G1 phase nuclei, but not with G2 phase nuclei. Y RNAs interact and colocalise with the origin recognition complex (ORC), the pre-replication complex (pre-RC) protein Cdt1, and other proteins implicated in the initiation of DNA replication. These data support a molecular ‘catch and release’ mechanism for Y RNA function during the initiation of chromosomal DNA replication, which is consistent with Y RNAs acting as replication licensing factors.