We have recently built a new polarimeter, PLANETPOL, designed to be sensitive to fractional polarizations as small as one part in a million. PLANETPOL is designed to be able to detect the small polarizations expected from the scattered light from a planetary atmosphere in an extrasolar planet system. On a recent run on the WHT we have demonstrated that PLANETPOL meets its design goal of measuring polarizations repeatably at a level of about 1 x 10-6. This is around 100 or more times better than previous instruments. We have found that the telescope polarization of the WHT is low (1.8 x 10-5). We also find that nearby normal stars have very low polarizations, implying that both their intrinsic and interstellar polarizations are low. I will describe the novel features of the PLANETPOL instrument that make possible its high sensitivity, and discuss the future potential of high sensitivity polarimetry.