  We present a new mechanism for thermally produced dark matter, based on a
semi-annihilation-like process, $\chi+ \chi +\text{SM} \rightarrow \chi +
\text{SM}$, with intriguing consequences for the properties of dark matter.
First, its mass is low, $\lesssim 1$ GeV (but $\gtrsim 5$ 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 $\chi+ \chi + \chi \rightarrow \chi + \chi$
models. Third, in the $3 \rightarrow 2$ 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. In particular, the Co-SIMP model for
thermal-relic dark matter can explain the XENON1T excess.
