Inelastic neutron scattering measurements of magnetic excitations in the charge-ordered state of Yb4As3 have been performed under magnetic field up to about 6 T. By applying a magnetic field, the spectrum at the one-dimensional wave vector q = 1 [ pi/d] changes drastically from a broad one corresponding to the spinon excitation continuum of the one-dimensional S = 1 / 2 spin system to a sharp one at a finite energy, indicating the opening of an energy gap in the system. The magnetic field dependence of the gap is well fitted by the power law H2/3. The experimental result gives strong evidence for the existence of a staggered field alternating along Yb3+ chains induced by the Dzyaloshinsky-Moriya interaction.