We have carried out a direct measurement of the degree of spin polarization (P) of the magnetic semiconductor Ga1-xMnxAs using Andreev reflection spectroscopy. Analyses of the conductance spectra of high transparency Ga(0.95)Mn(0.05)As/Ga junctions consistently yield an intrinsic value for P greater than 85%. Our experiments also revealed an extreme sensitivity of the measured spin polarization to the nature and quality of the interface for this material.