The stochastic variational method is used in conjunction with stabilization ideas to compute the low-energy s-wave phase shifts and scattering lengths for Ps-Ps scattering. The scattering lengths obtained were 8.44a0 for the singlet-singlet and 3.00a0 for the triplet-triplet states (the spin state refers to the coupling of the two electrons and the coupling of the two positrons in the system). The positive scattering length in the triplet-triplet channel means a stable Bose-Einstein condensate of triplet Ps atoms is physically possible. The large value of the 3Ps3Ps→1Ps1Ps cross section, 7.41πa02 suggests the use of spin-polarized positrons as advanced by Platzmann and Mills [Phys. Rev. B 49 454 (1994)].