  We report observations of the linear polarization of the WASP-18 system,
which harbors a very massive ( approx 10 M_J) planet orbiting very close to its
star with an orbital period of 0.94 days. We find the WASP-18 system is
polarized at about 200 parts-per-million (ppm), likely from the interstellar
medium predominantly, with no strong evidence for phase dependent modulation
from reflected light from the planet. We set an upper limit of 40 ppm (99%
confidence level) on the amplitude of a reflected polarized light planetary
signal. We compare the results with models for a number of processes that may
produce polarized light in a planetary system to determine if we can rule out
any phenomena with this limit. Models of reflected light from thick clouds can
approach or exceed this limit, but such clouds are unlikely at the high
temperature of the WASP-18b atmosphere. Additionally, we model the expected
polarization resulting from the transit of the planet across the star and find
this has an amplitude of about 1.6 ppm, which is well below our detection
limits. We also model the polarization due to the tidal distortion of the star
by the massive planet and find this is also too small to be measured currently.
