New evidence is presented for collimated outflow from a starburst nucleus in the edge-on galaxy NGC 3628. A plume of X-ray emission along the minor axis of this galaxy is suggested by the distribution of counts in the softer energy channels of the Einstein Observatory IPC. Plumes of H-alpha emission are visible in a CCD image of the southern minor axis region, at a position angle consistent with that of the X-ray plume, while extended, possibly filamentary, H-alpha emission is visible in the north. Optical spectroscopy along the northern minor axis clearly detects line emission, with line ratios of H-alpha, N II, and S II changing from those characteristic of normal H II regions near the nucleus, to a low-ionization state, consistent with shock heating, farther out. All this evidence, and the IR and radio continuum properties of this galaxy, make NGC 3628 another member of the growing class of galaxies with starburst nuclear activity and outflowing winds, to which NGC 253 and M82 already belong.