  We explore the LHC phenomenology of dark matter (DM) pair production in
association with a 125 GeV Higgs boson. This signature, dubbed `mono-Higgs,'
appears as a single Higgs boson plus missing energy from DM particles escaping
the detector. We perform an LHC background study for mono-Higgs signals at
$\sqrt{s} = 8$ and $14$ TeV for four Higgs boson decay channels:
$\gamma\gamma$, $b \bar b$, and $ZZ^* \to 4\ell$, $\ell\ell j j$. We estimate
the LHC sensitivities to a variety of new physics scenarios within the
frameworks of both effective operators and simplified models. For all these
scenarios, the $\gamma\gamma$ channel provides the best sensitivity, whereas
the $b\bar b$ channel suffers from a large $t \bar t$ background. Mono-Higgs is
unlike other mono-$X$ searches ($X$=jet, photon, etc.), since the Higgs boson
is unlikely to be radiated as initial state radiation, and therefore probes the
underlying DM vertex directly.
