  Certain strongly interacting dark matter candidates could have evaded
detection, and much work has been done on constraining their parameter space.
Recently, it was shown theoretically that the scattering cross section for
$m_\chi \gtrsim 1$ GeV pointlike dark matter with a nucleus cannot be
significantly larger than the geometric cross section of the nucleus. This
realization closes the parameter space for pointlike strongly interacting dark
matter. However, strongly interacting dark matter is still theoretically
possible for composite particles, with much parameter space open. We set new,
wide-ranging limits based on data from a novel detector at the University of
Chicago. Backgrounds are greatly suppressed by requiring coincidence detection
between two spatially separated liquid-scintillator modules. For dark matter
($v \sim 10^{-3}$c), the time of flight would be $\sim 2~\mu{\rm s}$, whereas
for cosmic rays, it would be $\sim 2~{\rm ns}$. We outline ways to greatly
increase sensitivity at modest costs.
