Lowest-order QED theory using distorted-wave states is applied to the calculation of positron-impact ionization cross sections for highly charged atomic ions. Electron and positron ionization cross sections for atomic ions are predicted to differ by substantial amounts in the threshold region. For highly charged ions like U +, the smaller positron ionization cross section is more strongly affected by transverse photon interactions than the corresponding electron ionization cross section. At twice the threshold for U + ionization, the annihilation terms are found to reduce the positron cross section by about 12%.PACS number(s): 34.80.Kw