We report on the experimental observation of tunneling across an ultrathin metallic Cr spacer layer that is inserted at the interface of a Fe/MgO/Fe(001) junction. We show how this remarkable behavior in a solid-state device reflects a quenching in the transmission of particular electronic states, as expected from the symmetry-filtering properties of the MgO barrier and the band structure of the bcc Cr(001) spacer in the epitaxial junction stack. This ultrathin Cr metallic barrier can promote quantum well states in an adjacent Fe layer.