We present a convergent variational basis-set calculational scheme for elas
tic scattering of the positronium atom by the hydrogen atom in S wave. High
ly correlated trial functions with appropriate symmetry are needed to achie
ve convergence. We report convergent results for scattering lengths in atom
ic units for both singlet (= 3.49 +/-0.20) and triplet (= 2.46 +/-0.10) sta
tes.