The production of antideuterons has been observed in electron-positron annihilations at center-of-mass energies around 10 GeV. Antideuterons have been identified unambiguously by their energy loss in the drift chamber, their time-of-flight and the pattern of their energy deposition in the shower counters of the ARGUS detector. The production rate in the momentum range (0.6?1.8) GeV/c is (1.6?0.7+1.0) × 10?5 per hadronic event.