Eukaryotic centromeres are maintained at specific chromosomal sites over many generations. In the budding yeast Saccharomyces cerevisiae, centromeres are genetic elements defined by a DNA sequence that is both necessary and sufficient for function; whereas, in most other eukaryotes, centromeres are maintained by poorly characterized epigenetic mechanisms in which DNA has a less definitive role. Here we use the pathogenic yeast Candida albicans as a model organism to study the DNA replication properties of centromeric DNA. By determining the genome-wide replication timing program of the C. albicans genome, we discovered that each centromere is associated with a replication origin that is the first to fire on its respective chromosome. Importantly, epigenetic formation of new ectopic centromeres (neocentromeres) was accompanied by shifts in replication timing, such that a neocentromere became the first to replicate and became associated with origin recognition complex (ORC) components. Furthermore, changing the level of the centromere-specific histone H3 isoform led to a concomitant change in levels of ORC association with centromere regions, further supporting the idea that centromere proteins determine origin activity. Finally, analysis of centromere-associated DNA revealed a replication-dependent sequence pattern characteristic of constitutively active replication origins. This strand-biased pattern is conserved, together with centromere position, among related strains and species, in a manner independent of primary DNA sequence. Thus, inheritance of centromere position is correlated with a constitutively active origin of replication that fires at a distinct early time. We suggest a model in which the distinct timing of DNA replication serves as an epigenetic mechanism for the inheritance of centromere position.