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We examine the distribution of elliptical galaxy intrinsic axis ratios, using the Ryden-Djorgovski sample of apparent axis ratios for 171 galaxies. Unlike previous studies, our technique is fully nonparametric, and places no a priori restrictions on the form of the ellipticity distribution. We find that the frequency function of intrinsic shapes implied by either the oblate or prolate hypotheses is negative at intrinsic axis ratios close to spherical. In other words, we can rule out the hypothesis of axisymmetry for this sample of galaxies. Allowing the intrinsic shapes to be triaxial yields a fully non-negative frequency function. We conclude that a strong case for triaxiality can be made purely on the basis of the distribution of apparent shapes.