We describe the HIgh Precision Polarimetric Instrument (HIPPI), a polarimeter built at UNSW (The University of New South Wales) Australia and used on the Anglo-Australian Telescope (AAT). HIPPI is an aperture polarimeter using a ferro-electric liquid crystal modulator. HIPPI measures the linear polarization of starlight with a sensitivity in fractional polarization of ~4 x 10... on low-polarization objects and a precision of better than 0.01 per cent on highly polarized stars. The detectors have a high dynamic range allowing observations of the brightest stars in the sky as well as much fainter objects. The telescope polarization of the AAT is found to be 48 plus or minus 5 x 10... in the g' band. (ProQuest: ... denotes formulae/symbols omitted.)