Direct dissociative recombination of ground-stateHeH+

${}_{}{}^3{}_{}{}^{}\mathrm{HeH}_{}^{+}{}_{}{}^{}$ molecular ions have been stored in an ion storage ring and allowed to interact with electrons from an electron cooler. Neutral reaction products have been counted and an absolute cross section for dissociative recombination has been measured. The spectrum reveals a prominent peak at about 18 eV and a weaker one at about 30 eV. The origin of the low-energy dissociative recombination of ${}_{}{}^3{}_{}{}^{}\mathrm{HeH}_{}^{+}{}_{}{}^{}$ is discussed, and the mechanism responsible for the high-energy peak is modeled by calculating the vibrational overlap between the ground state of the molecular ion and several repulsive states. It is concluded that ions populate primarily the singlet electronic ground state, and that the peaks at 18 and 30 eV arise predominantly from direct dissociative recombination of vibrationally cold ${}_{}{}^3{}_{}{}^{}\mathrm{HeH}_{}^{+}{}_{}{}^{}$.