We propose and experimentally demonstrate a reliable chromatic dispersion measurement method for installed optical fibers. This technique is based on a modified Sagnac interferometer which is polarization-independent, hence no polarization controller device is needed to control the polarization state of the light entering into the interferometer during measurement. In our proposed system, the polarization mode dispersion (PMD) of the test fiber is compensated by employing a Faraday rotator mirror at one end of the fiber, so that the measured dispersion results will not be affected by any external perturbations on the test fiber. In addition, our method is single-ended, rapid (<1 s), and accurate. Experimental results show the differences for dispersion and dispersion slope of only 0.17% and 1.24%, respectively, compared with that of a commercial instrument. All characteristics indicate that our approach is indeed suitable for in-field dispersion measurement of installed fibers.