The discovery of a 125 GeV Higgs boson at the Large Hadron Collider strongly motivates direct searches for additional Higgs bosons. In a type I two Higgs doublet model there is a large region of parameter space at $tanbeta > 5$ that is currently unconstrained experimentally. We show that the process $gg to H to A Z to ZZh$ can probe this region, and can be the discovery mode for an extended Higgs sector at the LHC. We analyze 9 promising decay modes for the $ZZh$ state, and we find that the most sensitive final states are $ellellellell bb$, $ellell jjbb$, $ellell u ugammagamma$ and $ellellellell +{}$missing energy.
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