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 macro and (3)He macro 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 (3)He macro freeze-out volume is smaller than the d macro freeze-out volume.