  We present high-precision linear polarization observations of four bright hot
Jupiter systems ($\tau$ Boo, HD 179949, HD 189733 and 51 Peg) and use the data
to search for polarized reflected light from the planets. The data for 51 Peg
are consistent with a reflected light polarization signal at about the level
expected with 2.8$\sigma$ significance and a false alarm probability of 1.9 per
cent. More data will be needed to confirm a detection of reflected light in
this system. HD 189733 shows highly variable polarization that appears to be
most likely the result of magnetic activity of the host star. This masks any
polarization due to reflected light, but a polarization signal at the expected
level of $\sim$20 ppm cannot be ruled out. $\tau$ Boo and HD 179949 show no
evidence for polarization due to reflected light. The results are consistent
with the idea that many hot Jupiters have low geometric albedos. Conclusive
detection of polarized reflected light from hot Jupiters is likely to require
further improvements in instrument sensitivity.
