The ground state hyperfine splitting of positronium, ΔHFS, is sensitive to high order corrections of QED. A new calculation up to O(α 3 lnα ) has revealed a 3.9 σ discrepancy between the QED prediction and the experimental results. This discrepancy might either be due to systematic problems in the previous experiments or to contributions beyond the Standard Model. We propose an experiment to measure ΔHFS employing new methods designed to remedy the possible systematic errors which may have affected the previous experiments. Our experiment will provide an independent check of the discrepancy. The prototype run has been performed and a result of ΔHFS = 203.3804 ± 0.0022 (stat., 11 ppm) ± 0.0081 (sys., 40 ppm) GHz has been obtained. Compensation magnets to obtain O(ppm) magnetic field uniformity has been developed. The final run will start soon and a measurement with a precision of O(ppm) is expected within a few years.