Telomeres, the natural ends of linear chromosomes, comprise repeat-sequence DNA and associated proteins. Replication of telomeres allows continued proliferation of human stem cells and immortality of cancer cells. This replication requires telomerase extension of the single-stranded DNA (ssDNA) of the telomeric G-strand ((TTAGGG)); the synthesis of the complementary C-strand ((CCCTAA)) is much less well characterized. The CST (CTC1-STN1-TEN1) protein complex, a DNA polymerase α-primase accessory factor, is known to be required for telomere replication in vivo, and the molecular analysis presented here reveals key features of its mechanism. We find that human CST uses its ssDNA-binding activity to specify the origins for telomeric C-strand synthesis by bound Polα-primase. CST-organized DNA polymerization can copy a telomeric DNA template that folds into G-quadruplex structures, but the challenges presented by this template probably contribute to telomere replication problems observed in vivo. Combining telomerase, a short telomeric ssDNA primer and CST-Polα-primase gives complete telomeric DNA replication, resulting in the same sort of ssDNA 3' overhang found naturally on human telomeres. We conclude that the CST complex not only terminates telomerase extension and recruits Polα-primase to telomeric ssDNA but also orchestrates C-strand synthesis. Because replication of the telomere has features distinct from replication of the rest of the genome, targeting telomere-replication components including CST holds promise for cancer therapeutics.