The fixed-core stochastic variational method has been used to demonstrate t
he existence of an electronically stable ground state for the Li(+)Ps(2) an
d Na(+)Ps(2) systems. The stability of Li(+)Ps(2) has been indicated previo
usly in an ab initio calculation by Varga, but the present estimate of the
binding energy is much closer to convergence. The Li(+)Ps(2) system has a b
inding energy of 0.013 149 Hartree and a 2 gamma annihilation rate of 3.86
x 10(9) s(-1). The Na(+)Ps(2) system has a binding energy of 0.005736 Hartr
ee and an annihilation rate of 4.02 x 10(9) s(-1). Examination of the inter
particle expectation values, correlation functions and the annihilation rat
es suggests that both of these systems can be best described as a Ps(2) mol
ecule weakly bound to an alkali atom cation.