  We report on the first nulling interferometric observations with the Large
Binocular Telescope Interferometer (LBTI), resolving the N' band (9.81 - 12.41
um) emission around the nearby main-sequence star eta Crv (F2V, 1-2 Gyr). The
measured source null depth amounts to 4.40% +/- 0.35% over a field-of-view of
140 mas in radius (~2.6\,AU at the distance of eta Corvi) and shows no
significant variation over 35{\deg} of sky rotation. This relatively low null
is unexpected given the total disk to star flux ratio measured by Spitzer/IRS
(~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 cannot 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
(~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).
