We present a new noninvasive technique for measuring the spatial variation of the zero-dispersion wavelength (lambda(0)) in single-mode fibers. This technique uses low-power continuous-wave lasers and is simple to implement. When applying this technique to dispersion-shifted fibers, we can resolve subnanometer fluctuations in lambda(0) with a potential spatial resolution of better than 100 m. We also discuss and show the limits of this and other techniques that arise from polarization-mode dispersion in the fibers.