Telomeres present unique challenges for genomes with linear chromosomes, including the inability of the semi-conservative DNA replication machinery to fully duplicate the ends of linear molecules. This is solved in virtually all eukaryotes by the enzyme telomerase, through the addition of telomeric repeats onto chromosome ends. It is widely assumed that the primary site of action for telomerase is the single-stranded G-rich overhang at the ends of chromosomes, formed after DNA replication is complete. We show here that the preferred substrate for telomerase in wild type yeast is instead a collapsed fork generated during replication of duplex telomeric DNA. Furthermore, newly collapsed forks are extensively elongated by telomerase by as much as ∼200 nucleotides in a single cell division, indicating that a major source of newly synthesized telomeric repeats in wild type cells occurs at collapsed forks. Fork collapse and the subsequent response by telomerase are coordinated by the dual activities of a telomere-dedicated RPA-like complex, which facilitates replication of duplex telomeric DNA and also recruits telomerase to the fork, thereby ensuring a high probability of re-elongation if DNA replication fails. We further show that the ability of telomerase to elongate newly collapsed forks is dependent on the Rad51 protein, indicating that telomerase activity in response to fork collapse proceeds through a regulatory pathway distinct from how telomerase engages fully replicated chromosome termini. We propose a new model in which spontaneous replication fork collapse and the subsequent response by telomerase is a major determinant of telomere length homeostasis.