We calculate the triton binding energy with a non-local NN potential that fits the world NN data below 350 MeV with the almost perfect χ 2 /datum of 1.03. The non-locality is derived from relativistic meson field theory. The result obtained in a 34-channel, charge-dependent Faddeev calculation is 8.00 MeV, which is 0.4 MeV above the predictions by local NN potentials. The increase in binding energy can be clearly attributed to the off-shell behavior of the non-local potential. Our result cuts in half the discrepancy between theory and experiment established from local NN potentials. Implications for other areas of microscopic nuclear structure, in which underbinding is a traditional problem, are discussed.