Studies in optical starlight have failed to reach a consensus on the importance of either galaxy interactions, bars, or nuclear spirals in triggering luminous active galactic nuclei (AGNs). Here, we present the first systematic imaging study of Seyfert (disk) galaxies in the 21-cm line of neutral atomic hydrogen (HI) gas. HI is the most sensitive and enduring tracer of galaxy interactions, and can reveal tidal features not otherwise visible in optical starlight. Our sample comprises all twenty-eight galaxies in the Wron-Cetty & Veron (1998) catalog with nuclear magnitudes -19 >= M-B > -23 (including Seyfert, LINER, and HII galaxies) at 0.015 <= z <= 0.017 in the northern hemisphere, and a matched control sample of twenty-seven inactive galaxies at z approximate to 0.008. We have detected nearly all the galaxies observed, and find a much higher incidence of tidal interactions-usually not seen in optical starlight-among the Seyfert galaxies by comparison with the matched control sample. Those Seyferts with uncertain or no clear tidal features show disturbed HI morphologies and/or kinematics, as well as HI companion galaxies, more frequently than the control sample. Our study suggests that the undisturbed optical appearence of active galaxies may be deceptive, and imply that galaxy-galaxy interactions trigger a significant fraction luminous AGNs at low redshifts. The majority of the Seyfert galaxies in our sample appear to be at a relatively early stage of an encounter rather than late in a merger.