We propose a novel mechanism for dark matter to explain the observed annual modulation signal at DAMA/LIBRA which avoids existing constraints from every other dark matter direct detection experiment including CRESST, CDMS, and XENON10. The dark matter consists of at least two light states with mass ~few GeV and splittings ~5 keV. It is natural for the heavier states to be cosmologically long-lived and to make up an O(1) fraction of the dark matter. Direct detection rates are dominated by the exothermic reactions in which an excited dark matter state down-scatters off of a nucleus, becoming a lower energy state. In contrast to (endothermic) inelastic dark matter, the most sensitive experiments for exothermic dark matter are those with light nuclei and low threshold energies. Interestingly, this model can also naturally account for the observed low-energy events at CoGeNT. The only significant constraint on the model arises from the DAMA/LIBRA unmodulated spectrum but it can be tested in the near future by a low-threshold analysis of CDMS-Si and possibly other experiments including CRESST, COUPP, and XENON100.

29 pages, 7 figures, minor updates and references added, version accepted by PRD