  We report the detection of asymmetry in the transit light curves of the
110-day period companion to KOI-368, a rapidly rotating A-dwarf. The
significant distortion in the transit light curve is attributed to spin-orbit
misalignment between the transiting companion and the gravity darkened host
star. Our analysis was based on 11 Long Cadence and 2 Short Cadence transits of
KOI-368.01 from the Kepler mission, as well as stellar parameters determined
from our follow-up spectroscopic observation. We measured the true obliquity
between the orbit normal and the stellar rotation axis to be 69 +9/-10 deg. We
also find a secondary eclipse event with depth 29 +/- 3 ppm at phase 0.59, from
which the temperature of the companion is constrained to 3060 +/- 50 K,
indicating that KOI-368.01 is a late M-dwarf. The eccentricity is also
calculated from the eclipse to be 0.1429 +/- 0.0007. The long period, high
obliquity, and low eccentricity of KOI-368.01 allow us to limit a number of
proposed theories for the misalignment of binary systems.
