The repair of DNA double-strand breaks (DSBs) can be hindered by the inability of repair factors to access damage sites in the tightly packaged chromatin. This study identifies a key role for the deacetylase sirtuin 6 (SIRT6) in facilitating chromatin relaxation and promoting repair. Toiber et al. observed that SIRT6 is rapidly recruited to DSBs, with much faster kinetics than previously reported. SIRT6 was shown to target the chromatin remodelling factor SNF2H to these sites and accelerate its association with them, as well as to deacetylate histone 3 at Lys56 (H3K56), which was required for SNF2H-mediated chromatin relaxation. Importantly, depletion of SIRT6 blocked downstream damage signalling, and loss of SIRT6, SNF2H or both proteins abolished repair by homologous recombination or resulted in defective repair by non-homologous end-joining.