We report "exact" quantum Monte Carlo calculations of the potential energy surface for the reaction H+H-2->H-2+H. The method used is free of systematic error. The statistical or sampling error was reduced to +/- 0.10 kcal/mol for several hundred points distributed across the surface, to +/- 0.02 kcal/mol for the minimum energy approach of H to H-2, to +/- 0.02 kcal/mol near the saddle point, and to +/- 0.01 kcal/mol at the saddle point. The upper and lower surfaces in the region of the Jahn-Teller cusp were determined with a statistical error of +/- 0.2 kcal/mol.