Solar ultraviolet light creates excited electronic states in DNA that can decay to mutagenic photoproducts. This vulnerability is compensated for in all organisms by enzymatic repair of photodamaged DNA. As repair is energetically costly, DNA is intrinsically photostable. Single bases eliminate electronic energy non-radiatively on a subpicosecond timescale, but base stacking and base pairing mediate the decay of excess electronic energy in the double helix in poorly understood ways. In the past, considerable attention has been paid to excited base pairs. Recent reports have suggested that light-triggered motion of a proton in one of the hydrogen bonds of an isolated base pair initiates non-radiative decay to the electronic ground state. Here we show that vertical base stacking, and not base pairing, determines the fate of excited singlet electronic states in single- and double-stranded oligonucleotides composed of adenine (A) and thymine (T) bases. Intrastrand excimer states with lifetimes of 50-150 ps are formed in high yields whenever A is stacked with itself or with T. Excimers limit excitation energy to one strand at a time in the B-form double helix, enabling repair using the undamaged strand as a template.