We present a new mechanism for thermally produced dark matter, based on a semi-annihilationlike process, χ + χ + SM → χ + SM, with intriguing consequences for the properties of dark matter. First, its mass is low, 1 GeV (but 5 keV to avoid structure-formation constraints). Second, it is strongly interacting, leading to kinetic equilibrium between the dark and visible sectors, avoiding the structure-formation problems of χ + χ + χ → χ + χ models. Third, in the 3 → 2 process, one dark matter particle is consumed, giving the standard-model particle a monoenergetic recoil. We show that this new scenario is presently allowed, which is surprising (perhaps a "minor miracle"). However, it can be systematically tested by novel analyses in present and near-term experiments.