Neutron scattering from copper benzoate, Cu(C6D5COO)2 3D2O, provides the first direct experimental evidence for field-dependent incommensurate low energy modes in a one-dimensional spin S = 1/2 antiferromagnet. Soft modes occur for wavevectors q=pi +- dq(H) where dq(H) ~ 2 pi M(H)/gmu_B as predicted by Bethe ansatz and spinon descriptions of the S = 1/2 chain. Unexpected was a field-induced energy gap $Delta(H) propto H^alpha$, where $alpha = 0.65(3)$ as determined from specific heat measurements. At H = 7 T (gmu_B H/J = 0.52), the magnitude of the gap varies from 0.06 - 0.3 J depending on the orientation of the applied field.