The mechanisms by which eukaryotic cells sense DNA double-strand breaks (DSBs) in order to initiate checkpoint responses are poorly understood. 53BP1 is a conserved checkpoint protein with properties of a DNA DSB sensor. Here, we solved the structure of the domain of 53BP1 that recruits it to sites of DSBs. This domain consists of two tandem tudor folds with a deep pocket at their interface formed by residues conserved in the budding yeast Rad9 and fission yeast Rhp9/Crb2 orthologues. In vitro, the 53BP1 tandem tudor domain bound histone H3 methylated on Lys 79 using residues that form the walls of the pocket; these residues were also required for recruitment of 53BP1 to DSBs. Suppression of DOT1L, the enzyme that methylates Lys 79 of histone H3, also inhibited recruitment of 53BP1 to DSBs. Because methylation of histone H3 Lys 79 was unaltered in response to DNA damage, we propose that 53BP1 senses DSBs indirectly through changes in higher-order chromatin structure that expose the 53BP1 binding site.