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The first measurements of light antinucleus production in Au+Au collisions at the Relativistic Heavy-Ion Collider are reported. The observed production rates for d-bar and 3He-bar are much larger than in lower energy nucleus-nucleus collisions. A coalescence model analysis of the yields indicates that there is little or no increase in the antinucleon freeze-out volume compared to collisions at CERN SPS energy. These analyses also indicate that the 3He-bar freeze-out volume is smaller than the d-bar freeze-out volume.