I will describe a new instrument project which has recently been funded by PPARC in the UK. We plan to build a very high sensitivity polarimeter which can detect polarization at levels of a few times 10^-7, about 100 times better than the best achieved with existing stellar polarimeters. We aim to use the instrument to detect the polarization of light scattered from the atmospheres of "hot Jupiter" type planets, and thereby achieve the first direct detection of extrasolar planets by means of their reflected light. I will describe the design of the new instrument, why we believe it is possible to achieve such high sensitivity, why existing instruments fall so far short of this performance, and what we will be able to learn about extrasolar planets.