Summary form only given. We present a novel use of a Sagnac interferometer (SI) for easy and accurate measurement of chromatic dispersion in long single-mode fiber. The interferometer contains within the ring an off-centered phase modulator as well as the fiber whose dispersion needs to be measured. The asymmetric location of the modulator with respect to the test fiber causes counter-propagating waves to travel with different propagation constants through the test fiber, and the dispersion is measured from the interference fringe