  PTFO 8-8695b represents the first transiting exoplanet candidate orbiting a
pre-main-sequence star. We find that the unusual lightcurve shapes of PTFO
8-8695 can be explained by transits of a planet across an oblate,
gravity-darkened stellar disk. We simultaneously and self-consistently fit two
separate lightcurves observed in 2009 December and 2010 December. Our two
self-consistent fits yield M_p = 3.0 M_Jup and M_p = 3.6 M_Jup for assumed
stellar masses of M_* = 0.34 M_Sun and M_* = 0.44 M_Sun respectively. The two
fits have precession periods of 293 days and 581 days. These mass
determinations (consistent with previous upper limits) along with the strength
of the gravity-darkened precessing model together validate PTFO 8-8695b as just
the second Hot Jupiter known to orbit an M-dwarf. Our fits show a high degree
of spin-orbit misalignment in the PTFO 8-8695 system: 69 +/- 2 or 73.1 +/- 0.5
degrees, in the two cases. The large misalignment is consistent with the
hypothesis that planets become Hot Jupiters with random orbital plane
alignments early in a system's lifetime. We predict that as a result of the
highly misaligned, precessing system, the transits should disappear for months
at a time over the course of the system's precession period. The precessing,
gravity-darkened model also predicts other observable effects: changing orbit
inclination that could be detected by radial velocity observations, changing
stellar inclination that would manifest as varying v sin i, changing projected
spin-orbit alignment that could be seen by the Rossiter-McLaughlin effect,
changing transit shapes over the course of the precession, and differing
lightcurves as a function of wavelength. Our measured planet radii of 1.64
R_Jup and 1.68 R_Jup in each case are consistent with a young,
hydrogen-dominated planet that results from a hot-start formation mechanism.
