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For 40 years, uniformly filled ellipsoidal beam distributions have been studied theoretically, as they hold the promise of generating self-fields linear in the coordinate offset in all three directions. Recently, a scheme for producing such distributions, based on the strong longitudinal expansion of an initially very short beam under its own space-charge forces, has been proposed. In this Letter we present the experimental demonstration of this scheme, obtained by illuminating the cathode in a rf photogun with an ultrashort laser pulse (approximately 35 fs rms) with an appropriate transverse profile. The resulting 4 MeV beam spatiotemporal (x,t) distribution is imaged using a rf deflecting cavity with 50 fs resolution. A temporal asymmetry in the ellipsoidal profile, due to image charge effects at the photocathode, is observed at higher charge operation. This distortion is also found to degrade the transverse beam quality.