We describe a method, based on the phase mismatch of four-wave mixing, for direct and accurate measurement of the dispersion map, D(lambda, z), of an optical fiber. The method, which requires no wavelength scanning and access to only one end of the fiber, has produced the data for an entire 34-km span, including hundreds of repetitions for signal averaging, in less than 0.25 s. Spatial resolution and accuracy in that first experimental test were ~1 km and deltaD ~ +/-0.03 ps/(nm km), respectively.