  We present a variational basis-set calculational scheme for elastic
scattering of positronium atom by helium atom in S wave and apply it to the
calculation of the scattering length. Highly correlated trial functions with
appropriate symmetry are used in this calculation. We report numerical result
for the scattering length in atomic unit: $(1.0\pm 0.1)a_0$. This corresponds
to a zero-energy elastic cross section of $(4.0\pm 0.8)\pi a_0^2$.
