  We have determined a dynamical mass for the companion to HD 33636 which
indicates it is a low-mass star instead of an exoplanet. Our result is based on
an analysis of Hubble Space Telescope (HST) astrometry and ground-based radial
velocity data. We have obtained high-cadence radial velocity measurements
spanning 1.3 years of HD 33636 with the Hobby-Eberly Telescope at McDonald
Observatory. We combined these data with previously published velocities to
create a data set that spans nine years. We used this data set to search for,
and place mass limits on, the existence of additional companions in the HD
33636 system. Our high-precision astrometric observations of the system with
the HST Fine Guidance Sensor 1r span 1.2 years. We simultaneously modeled the
radial velocity and astrometry data to determine the parallax, proper motion,
and perturbation orbit parameters of HD 33636. Our derived parallax, pi = 35.6
+/- 0.2 mas, agrees within the uncertainties with the Hipparcos value. We find
a perturbation period P = 2117.3 +/- 0.8 days, semimajor axis a_A = 14.2 +/-
0.2 mas, and system inclination i = 4.1 +/- 0.1 deg. Assuming the mass of the
primary star M_A = 1.02 +/- 0.03 M_sun, we obtain a companion mass M_B = 142
+/- 11 M_jup = 0.14 +/- 0.01 M_sun. The much larger true mass of the companion
relative to its minimum mass estimated from the spectroscopic orbit parameters
(M sin i = 9.3 M_jup) is due to the near face-on orbit orientation. This result
demonstrates the value of follow-up astrometric observations to determine the
true masses of exoplanet candidates detected with the radial velocity method.
