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A new interferometric method which indirectly measures the total chromatic dispersion of a single mode fiber is demonstrated. The technique utilizes a short length of fiber, an unmodulated broadband source, simple low frequency electronics, and a standard interferometer. The concept of this measurement is based on the behavior of the uncorrelated individual bursts of light from the elemental emitters that constitute a thermal source. Their propagation through a dispersive media, e.g., silica fiber, which is placed in one arm of the interferometer, is delayed and broadened. They will interfere with their counterpart from the other arm, generating a train of time-varying fringes as one mirror of the interferometer is uniformly translated. The local frequency of the fringes at a given position of the moving mirror is a direct measure of the instantaneous wavelength, while the mirror position itself demarks the corresponding relative delay. A colinearly launched HeNe laser beam is used as a reference to calibrate the other source's fringe width and location of the mirror. In this experiment, an edge-emitting LED of λo = 830 nm and Δλ = 60 nm was used. The tested fibers had a length of 27.9 cm and 38.3 cm, which made the width of the crosscorrelation function approximately 100 times greater than the source's coherence length. The speed of the mechanically driven mirror set the frequency of the HeNe fringes to approximately 800 Hz with an r.m.s. fluctuation around the mean of 0.2%. The SNR of the HeNe fringes was four times larger than the LED's. Ten different runs for each fiber were executed. Data from the two sets of simultaneous measurements of delay versus wavelength were used to fit the best linear and quadratic polynomials with a minimum residual mean error square. The derivative of this function with respect to wavelength gave the dispersion relation. The accuracy of measured delay and wavelength were 0.1 ps and 6 nm, respectively. The dispersion value and its standard error for the best linear fit was approximately 117 ∓ 2 ps/km nm. The standard error for the quadratic fit was much larger due to the high noise level accompanying signal. A thorough investigation of the noise sources, accuracies, standard error of the polynomial's coefficient, and SNR analysis is conducted. This measurement is simple and has the potential of achieving substantially higher accuracy--especially for the longer wavelength region where dispersion is minute.