We report on the first nulling interferometric observations with the Large Binocular Telescope Interferometer ( LBTI ) , resolving the N ’ band ( 9.81 - 12.41 \mu m ) emission around the nearby main-sequence star \eta Crv ( F2V , 1-2 Gyr ) . The measured source null depth amounts to 4.40 % \pm 0.35 % over a field-of-view of 140 mas in radius ( \sim 2.6 AU at the distance of \eta Crv ) and shows no significant variation over 35 ^ { \circ } of sky rotation . This relatively low null is unexpected given the total disk to star flux ratio measured by Spitzer/IRS ( \sim 23 % across the N ’ band ) , suggesting that a significant fraction of the dust lies within the central nulled response of the LBTI ( 79 mas or 1.4 AU ) . Modeling of the warm disk shows that it can not resemble a scaled version of the Solar zodiacal cloud , unless it is almost perpendicular to the outer disk imaged by Herschel . It is more likely that the inner and outer disks are coplanar and the warm dust is located at a distance of 0.5-1.0 AU , significantly closer than previously predicted by models of the IRS spectrum ( \sim 3 AU ) . The predicted disk sizes can be reconciled if the warm disk is not centrosymmetric , or if the dust particles are dominated by very small grains . Both possibilities hint that a recent collision has produced much of the dust . Finally , we discuss the implications for the presence of dust at the distance where the insolation is the same as Earth ’ s ( 2.3 AU ) .