  The confined variational method in conjunction with the orthogonalizing
pseudo-potential method and the stabilization method is used to study the low
energy elastic scattering between two spin-polarized metastable positronium
Ps(2\,$^{3}\!S_1$) atoms. Explicitly correlated Gaussian basis functions are
adopted to properly describe the complicated Coulomb interaction among the four
charged particles. The calculated $s$-wave scattering length
($\approx8.5\,a_0$) is positive, indicating the possibility of forming a stable
Bose-Einstein condensate of fully spin-polarized $\text{Ps}(2\,^{3}\!S_1)$
atoms. Our results will open a new way of experimental realization of Ps
condensate and development of $\gamma$-ray and $\text{Ps}(2\,^{3}\!S_1)$ atom
lasers.
