We present a new paradigm for achieving thermal relic dark matter. The mechanism arises when a nearly secluded dark sector is thermalized with the Standard Model after reheating. The freezeout process is a number-changing 3 \to 2 annihilation of strongly-interacting-massive-particles (SIMPs) in the dark sector, and points to sub-GeV dark matter. The couplings to the visible sector, necessary for maintaining thermal equilibrium with the Standard Model, imply measurable signals that will allow coverage of a signifi.cant part of the parameter space with future indirect and direct detection experiments and via direct production of dark matter at colliders. Moreover, 3 \to 2 annihilations typically predict sizable 2 \to 2 self-interactions which naturally address the `core vs. cusp' and `too-big-to-fail' small structure problems.