Using systematic sequences of correlation consistent Gaussian basis sets from double to sextuple zeta quality, the classical barrier height of the H+H-2 exchange reaction has been calculated by multireference configuration interaction (MRCI) methods. The MRCI calculations for collinear H-3 have also been calibrated against large basis set full CI (FCI) results, which demonstrate that the MRCI treatment leads to energies less than 1 mu hartree (<0.001 kcal/mol) above the FCI energies. The dependence of both the H-2 and H-3 total energies on the basis set is found to be very regular, and this behavior has been used to extrapolate to the complete basis set (CBS) limits. The resulting estimate of the H-H-H CBS limit yields a classical barrier height, relative to exact H+H-2, of 9.60+/-0.02 kcal/mol; the best directly calculated value for the barrier is equal to 9.62 kcal/mol. These results are in excellent agreement with recent quantum Monte Carlo calculations.