Time-of-flight neutron data reveal spin waves in the ferromagnetic ground state of the kagome staircase material Co₃V₂O₈. While previous work has treated this material as quasi–two-dimensional, we find that an inherently three-dimensional description is needed to describe the spin wave spectrum throughout reciprocal space. Moreover, spin wave branches show gaps that point to an unexpectedly large Dzyaloshinskii-Moriya interaction on the nearest-neighbor bond, with D₁ ≥ J₁/2. A better understanding of the Dzyaloshinskii-Moriya interaction in this material should shed light on the multiferroicity of the related Ni₃V₂O₈. At a higher temperature where Co₃V₂O₈ displays an antiferromagnetic spin density wave structure, there are no well-defined spin wave excitations, with most of the spectral weight observed in broad diffuse scattering centered at the (0, 0.5, 0) antiferromagnetic Bragg peak.