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: $gammagamma$, $b bar b$, and $ZZ^* to 4ell$, $ellell j j$. 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 $gammagamma$ channel provides the best sensitivity, whereas the $bbar b$ 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.