Accumulating evidence suggests that RNAs interacting with genomic regions play important roles in the regulation of genome functions, including X chromosome inactivation and gene expression. However, to our knowledge, no non-biased methods of identifying RNAs that interact with a specific genomic region have been reported. Here, we used enChIP-RNA-Seq, a combination of engineered DNA-binding molecule-mediated chromatin immunoprecipitation (enChIP) and RNA sequencing (RNA-Seq), to perform a non-biased search for RNAs interacting with telomeres. In enChIP-RNA-Seq, the target genomic regions are captured using an engineered DNA-binding molecule such as a transcription activator-like protein. Subsequently, RNAs that interact with the target genomic regions are purified and sequenced. The RNAs detected by enChIP-RNA-Seq contained known telomere-binding RNAs, including the telomerase RNA component (Terc), the RNA component of mitochondrial RNA processing endoribonuclease (Rmrp), and Cajal body-specific RNAs. In addition, a number of novel telomere-binding non-coding RNAs were also identified. Binding of two candidate non-coding RNAs to telomeres was confirmed by immunofluorescence microscopy and RNA fluorescence in situ hybridization (RNA-FISH) analyses. The novel telomere-binding non-coding RNAs identified here may play important roles in telomere functions. To our knowledge, this study is the first non-biased identification of RNAs associated with specific genomic regions. The results presented here suggest that enChIP-RNA-Seq analyses are useful for the identification of RNAs interacting with specific genomic regions, and may help to contribute to current understanding of the regulation of genome functions.