Telomeres-repeated, noncoding nucleotide motifs and associated proteins that are found at the ends of eukaryotic chromosomes-mediate genome stability and determine cellular lifespan(1). Telomeric-repeat-containing RNA (TERRA) is a class of long noncoding RNAs (lncRNAs) that are transcribed from chromosome ends(2,3); these RNAs in turn regulate telomeric chromatin structure and telomere maintenance through the telomere-extending enzyme telomerase(4-6) and homology-directed DNA repair(7,8). The mechanisms by which TERRA is recruited to chromosome ends remain poorly defined. Here we develop a reporter system with which to dissect the underlying mechanisms, and show that the UUAGGG repeats of TERRA are both necessary and sufficient to target TERRA to chromosome ends. TERRA preferentially associates with short telomeres through the formation of telomeric DNA-RNA hybrid (R-loop) structures that can form in trans. Telomere association and R-loop formation trigger telomere fragility and are promoted by the recombinase RAD51 and its interacting partner BRCA2, but counteracted by the RNA-surveillance factors RNaseH1 and TRF1. RAD51 physically interacts with TERRA and catalyses R-loop formation with TERRA in vitro, suggesting a direct involvement of this DNA recombinase in the recruitment of TERRA by strand invasion. Together, our findings reveal a RAD51-dependent pathway that governs TERRA-mediated R-loop formation after transcription, providing a mechanism for the recruitment of lncRNAs to new loci in trans.