The half-life of tritium has been measured by monitoring the decay of the x-ray bremsstrahlung emitted by gaseous mixtures of (H-2)-H-3 and Xe. The result, 12.31 +/- 0.03 yr, when combined with the end-point energy measured on the same sources, yields the product (G(A)/G(V)')<sigma> = 2.098 +/- 0.003, where <sigma> is the Gamow-Teller matrix element. Combined with a recent precise calculation of the matrix element, this value suggests that the renormalization of the axial-vector interaction can be entirely accounted for by nuclear effects in the triton. The deduced value of G(A)/G(V)' constrains the neutron lifetime to lie in the range of 897 +/- 3 s.
