  The Large Binocular Telescope Interferometer (LBTI) is a versatile instrument
designed for high-angular resolution and high-contrast infrared imaging (1.5-13
microns). In this paper, we focus on the mid-infrared (8-13 microns) nulling
mode and present its theory of operation, data reduction, and on-sky
performance as of the end of the commissioning phase in March 2015. With an
interferometric baseline of 14.4 meters, the LBTI nuller is specifically tuned
to resolve the habitable zone of nearby main-sequence stars, where warm
exozodiacal dust emission peaks. Measuring the exozodi luminosity function of
nearby main-sequence stars is a key milestone to prepare for future exoEarth
direct imaging instruments. Thanks to recent progress in wavefront control and
phase stabilization, as well as in data reduction techniques, the LBTI
demonstrated in February 2015 a calibrated null accuracy of 0.05% over a
three-hour long observing sequence on the bright nearby A3V star beta Leo. This
is equivalent to an exozodiacal disk density of 15 to 30 zodi for a Sun-like
star located at 10pc, depending on the adopted disk model. This result sets a
new record for high-contrast mid-infrared interferometric imaging and opens a
new window on the study of planetary systems.
