Telomere replication is achieved through the combined action of the conventional DNA replication machinery and the reverse transcriptase, telomerase. Telomere-binding proteins have crucial roles in controlling telomerase activity; however, little is known about their role in controlling semi-conservative replication, which synthesizes the bulk of telomeric DNA. Telomere repeats in the fission yeast Schizosaccharomyces pombe are bound by Taz1, a regulator of diverse telomere functions. It is generally assumed that telomere-binding proteins impede replication fork progression. Here we show that, on the contrary, Taz1 is crucial for efficient replication fork progression through the telomere. Using two-dimensional gel electrophoresis, we find that loss of Taz1 leads to stalled replication forks at telomeres and internally placed telomere sequences, regardless of whether the telomeric G-rich strand is replicated by leading- or lagging-strand synthesis. In contrast, the Taz1-interacting protein Rap1 is dispensable for efficient telomeric fork progression. Upon loss of telomerase, taz1Delta telomeres are lost precipitously, suggesting that maintenance of taz1Delta telomere repeats cannot be sustained through semi-conservative replication. As the human telomere proteins TRF1 and TRF2 are Taz1 orthologues, we predict that one or both of the human TRFs may orchestrate fork passage through human telomeres. Stalled forks at dysfunctional human telomeres are likely to accelerate the genomic instability that drives tumorigenesis.