Tomato Yellow Leaf Curl Virus Disease incited by Tomato yellow leaf curl virus (TYLCV) causes huge losses in tomato production worldwide and is caused by different related begomovirus species. Breeding for TYLCV resistance has been based on the introgression of multiple resistance genes originating from several wild tomato species. In this study we have fine-mapped the widely used Solanum chilense-derived Ty-1 and Ty-3 genes by screening nearly 12,000 plants for recombination events and generating recombinant inbred lines. Multiple molecular markers were developed and used in combination with disease tests to fine-map the genes to a small genomic region (approximately 70 kb). Using a Tobacco Rattle Virus-Virus Induced Gene Silencing approach, the resistance gene was identified. It is shown that Ty-1 and Ty-3 are allelic and that they code for a RNA-dependent RNA polymerase (RDR) belonging to the RDRγ type, which has an atypical DFDGD motif in the catalytic domain. In contrast to the RDRα type, characterized by a catalytic DLDGD motif, no clear function has yet been described for the RDRγ type, and thus the Ty-1/Ty-3 gene unveils a completely new class of resistance gene. Although speculative, the resistance mechanism of Ty-1/Ty-3 and its specificity towards TYLCV are discussed in light of the function of the related RDRα class in the amplification of the RNAi response in plants and transcriptional silencing of geminiviruses in plants.