DNA replication is needed to duplicate a cell’s genome in S phase and segregate it during cell division. Previous work inLeishmaniadetected DNA replication initiation at just a single region in each chromosome, an organisation predicted to be insufficient for complete genome duplication within S phase. Here, we show that acetylated histone H3 (AcH3), base J and a kinetochore factor co-localise in each chromosome at only a single locus, which corresponds with previously mapped DNA replication initiation regions and is demarcated by localised G/T skew and G4 patterns. In addition, we describe previously undetected subtelomeric DNA replication in G2/M and G1-phase-enriched cells. Finally, we show that subtelomeric DNA replication, unlike chromosome-internal DNA replication, is sensitive to hydroxyurea and dependent on 9-1-1 activity. These findings indicate thatLeishmania’s genome duplication programme employs subtelomeric DNA replication initiation, possibly extending beyond S phase, to support predominantly chromosome-internal DNA replication initiation within S phase.