We have developed a star-and-sky chopping polarimeter for accurate measurements of linear polarization of starlight in the standard astronomical photometric U, B, V, R, and I bands. The instrumental polarization, as determined by observing the standard unpolarized stars, is 0.04%. It is possible to use the instrument for the measurements of circular polarization as well. A UNICORN microcomputer controls the various operations of the instrument, acquires the data, and does the on-line data reduction. This paper describes the design and performance of the polarimeter.