We describe a novel method, based on asymmetric modulation in a Sagnac interferometer, that measures the chromatic dispersion of single-mode fibers. The interferometer incorporates a phase modulator and a test fiber, so the dispersion can be determined from the interference fringe seen when a sweep rf signal is applied to the modulator. This technique provides picosecond temporal resolution without the need for any fast diagnostic equipment and is capable of accurately measuring the average dispersion of fibers several kilometers long.