A simple and accurate method is proposed for characterizing the chromatic dispersion of high air-filling fraction photonic crystal fibers. The method is based upon scalar modulation instability generated by a strong pump wave propagating near the zero-dispersion wavelength. Measuring the modulation instability sideband frequency shifts as a function of wavelength gives a direct measurement of the fiber's chromatic dispersion over a wide wavelength range. To simplify the dispersion calculation we introduce a simple analytical model of the fiber's dispersion, and verify its accuracy via a full numerical simulation. Measurements of the chromatic dispersion of two different types of high air-filling fraction photonic crystal fibers are presented.