Next-generation DNA sequencing promises to revolutionize clinical medicine and basic research. However, while this technology has the capacity to generate hundreds of billions of nucleotides of DNA sequence in a single experiment, the error rate of ~1% results in hundreds of millions of sequencing mistakes. These scattered errors can be tolerated in some applications but become extremely problematic when "deep sequencing" genetically heterogeneous mixtures, such as tumors or mixed microbial populations. To overcome limitations in sequencing accuracy, we have developed a method termed Duplex Sequencing. This approach greatly reduces errors by independently tagging and sequencing each of the two strands of a DNA duplex. As the two strands are complementary, true mutations are found at the same position in both strands. In contrast, PCR or sequencing errors result in mutations in only one strand and can thus be discounted as technical error. We determine that Duplex Sequencing has a theoretical background error rate of less than one artifactual mutation per billion nucleotides sequenced. In addition, we establish that detection of mutations present in only one of the two strands of duplex DNA can be used to identify sites of DNA damage. We apply the method to directly assess the frequency and pattern of random mutations in mitochondrial DNA from human cells.