  The Transit Timing Variations (TTVs) can be used as a diagnostic of
gravitational interactions between planets in a multi-planet system. Many
Kepler Objects of Interest (KOIs) exhibit significant TTVs, but KOI-142.01
stands out among them with an unrivaled, 12-hour TTV amplitude. Here we report
a thorough analysis of KOI-142.01's transits. We discover periodic Transit
Duration Variations (TDVs) of KOI-142.01 that are nearly in phase with the
observed TTVs. We show that KOI-142.01's TTVs and TDVs uniquely detect a
non-transiting companion with a mass 0.7 that of Jupiter (KOI-142c).
KOI-142.01's mass inferred from the transit variations is consistent with the
measured transit depth, suggesting a Neptune class planet (KOI-142b). The
orbital period ratio P_c/P_b=2.03 indicates that the two planets are just wide
of the 2:1 resonance. The present dynamics of this system, characterized here
in detail, can be used to test various formation theories that have been
proposed to explain the near-resonant pairs of exoplanets.
