We present measurements of the inclusive production of antideuterons in e + e − annihilation into hadrons at ≈ 10.58     GeV center-of-mass energy and in Υ ( 1 S , 2 S , 3 S ) decays. The results are obtained using data collected by the BABAR detector at the PEP-II electron-positron collider. Assuming a fireball spectral shape for the emitted antideuteron momentum, we find B ( Υ ( 1 S ) → ¯ d X ) = ( 2.81 ± 0.49 ( stat ) + 0.20 − 0.24 ( syst ) ) × 10 − 5 , B ( Υ ( 2 S ) → ¯ d X ) = ( 2.64 ± 0.11 ( stat ) + 0.26 − 0.21 ( syst ) ) × 10 − 5 , B ( Υ ( 3 S ) → ¯ d X ) = ( 2.33 ± 0.15 ( stat ) + 0.31 − 0.28 ( syst ) ) × 10 − 5 , and σ ( e + e − → ¯ d X ) = ( 9.63 ± 0.41 ( stat ) + 1.17 − 1.01 ( syst )     fb .