We describe a high resolution laser polarimeter built from commodity optical components. The optical rotation angle is determined by measuring the phase difference between two harmonically modulated polarised laser beams - an 'object beam' that passes through the sample under test and a 'reference beam' that bypasses the sample. The complete polarimeter may be assembled from low cost off-the-shelf parts for less than £300 (UK Sterling). Data acquisition and analysis are carried out on a microcontroller running an efficient algorithm based on the sliding Discrete Fourier Transform. Despite its low cost, the polarimeter is a fully automatic, research-grade instrument with an accuracy of ±0.0013° and a precision of ±0.0028° - comparable to far costlier commercial instruments. The polarimeter's ease of use, compact size, fast measurement times and high angular resolution make it a capable and versatile tool for analytical science, while its low cost means it is ideally suited for use in resource-constrained environments and process monitoring. The polarimeter is released here as open hardware, with technical diagrams, a full parts list, and source code for its firmware included as Supplementary Information.