Using a unique method we present accurate quantitative measurements of the Ostwald ripening of an emulsion system. Time-resolved small-angle neutron scattering monitors the time evolution of the average radius and number density of the emulsion drops. The results qualitatively agree with the current theory of Ostwald ripening but there is a quantitative, experimentally significant, discrepancy of a factor of 1.7. We argue that these accurate experiments, performed on a well characterized system, provide a most useful basis for testing further refinements of the theory.