  We present a convergent variational basis-set calculational scheme for
elastic scattering of positronium atom by hydrogen atom in S wave. Highly
correlated trial functions with appropriate symmetry are needed for achieving
convergence. We report convergent results for scattering lengths in atomic
units for both singlet ($=3.49\pm 0.20$) and triplet ($=2.46\pm 0.10$) states.
