We have observed negative differential resistance (NDR) and large peak current densities in a novel resonant interband tunneling structure grown by molecular beam epitaxy in the InAs/GaSb/AlSb material system. The structure consists of a thin AlSb barrier layer displaced from an InAs(n)/GaSp(p) interface. NDR is readily observable at room temperature with peak current densities greater than 105A/cm2. The enhancement in peak current density relative to a structure with no AlSb barrier is consistent with the existence of a quasi‐bound state in the region between the barrier and the InAs/GaAs interface. Furthermore, we demonstrate that by growing the AlSb layer on either the InAs or GaSb side of the interface, the quasi‐bound state can be localized in either material.