The fixed-core stochastic variational method has been used to demonstrate the existence of an electronically stable ground state for the Li+Ps2 and Na+Ps2 systems. The stability of Li+Ps2 has been indicated previously in an ab initio calculation by Varga, but the present estimate of the binding energy is much closer to convergence. The Li+Ps2 system has a binding energy of 0.013 149 Hartree and a 2 annihilation rate of 3.86 ? 109 s-1. The Na+Ps2 system has a binding energy of 0.005 736 Hartree and an annihilation rate of 4.02 ? 109 s-1. Examination of the interparticle expectation values, correlation functions and the annihilation rates suggests that both of these systems can be best described as a Ps2 molecule weakly bound to an alkali atom cation.