The stochastic variational method (SVM) is used in conjunction with stabilization ideas in order to compute low-energy phase shifts. The method is tested by applying it to a simple model problem, and to s-wave positron-hydrogen scattering. The SVM is then applied to the calculation of the s- and p-wave phase shifts for Ps-H scattering. The scattering lengths obtained were 4.34a(0) for the electronic-spin-singlet state and 2.22a(0) for the triplet state. The present scattering lengths are probably accurate to +/-3% and are the most accurate that have so far been computed for the Ps-H systems.