Little is known about the dynamics of chromosomes in interphase nuclei. By tagging four chromosomal regions with a green fluorescent protein fusion to lac repressor, we monitored the movement and subnuclear position of specific sites in the yeast genome, sampling at short time intervals. We found that early and late origins of replication are highly mobile in G1 phase, frequently moving at or faster than 0.5 micrometers/10 seconds, in an energy-dependent fashion. The rapid diffusive movement of chromatin detected in G1 becomes constrained in S phase through a mechanism dependent on active DNA replication. In contrast, telomeres and centromeres provide replication-independent constraint on chromatin movement in both G1 and S phases.