We have measured the cross section for the important fusion-energy reaction H(t, a)n at 17 energies over the triton bombarding energy range of 12.5 -117 keV. This corresponds to an equivalent deuteron bombarding energy range of 8.3 -78.1 keV and to a plasma temperature (kT) range of 0.7 -18.8 keV. The cross section is accurate to 1.4% over most of the energy range, with the error rising to 4.8% at the lowest energy. These data are considerably more accurate than the previous d+ t measurements in this energy range. We compare our data with those of other measurements and with an existing R-matrix analysis of the mass-5 system. We have also performed a single-level R-matrix analysis of a restricted data base that contains our data and have used that analysis to compute Maxwellian reactivities up to a plasma temperature of 20 keV. In addition, for calibration purposes, we measured to better than 1% absolute error the H(p, p) H elastic differential cross section at six laboratory angles at a proton bombarding energy of 10.04 MeV.