The dissociative ionization of organic molecules, induced by positrons having energies below the positronium threshold (0.5 -3 eV), has been studied. Cross sections for the ionization-&agmentation processes increase as positron energies decrease. The data reveal that the energy required for dissociative ionization is supplied by the annihilation process, and that fragmentation occurs by breakage of C -C single bonds in preference to double and triple bonds.PACS number(s): 34.80. Dp, 36.10.Dr, 78.70.Bj