  Planets in highly eccentric orbits form a class of objects not seen within
our Solar System. The most extreme case known amongst these objects is the
planet orbiting HD~20782, with an orbital period of 597~days and an
eccentricity of 0.96. Here we present new data and analysis for this system as
part of the Transit Ephemeris Refinement and Monitoring Survey (TERMS). We
obtained CHIRON spectra to perform an independent estimation of the fundamental
stellar parameters. New radial velocities from AAT and PARAS observations
during periastron passage greatly improve our knowledge of the eccentric nature
of the orbit. The combined analysis of our Keplerian orbital and Hipparcos
astrometry show that the inclination of the planetary orbit is $> 1.22\degr$,
ruling out stellar masses for the companion. Our long-term robotic photometry
show that the star is extremely stable over long timescales. Photometric
monitoring of the star during predicted transit and periastron times using MOST
rule out a transit of the planet and reveal evidence of phase variations during
periastron. These possible photometric phase variations may be caused by
reflected light from the planet's atmosphere and the dramatic change in
star--planet separation surrounding the periastron passage.
