We present observations of PS16dtm (also known as SN 2016ezh), a luminous transient that occurred at the nucleus of a narrow-line Seyfert 1 galaxy hosting a 106 M black hole. The light curve shows that PS16dtm exhibited a plateau phase for ∼100 days, during which it showed no color evolution, maintained a blackbody temperature of K, and radiated at approximately the Eddington luminosity of the supermassive black hole (SMBH). The spectra exhibit multicomponent hydrogen emission lines and strong Fe ii emission, show little time evolution, and closely resemble the spectra of NLS1s while being distinct from those of Type IIn supernovae (SNe IIn). Moreover, PS16dtm is undetected in the X-rays to a limit an order of magnitude below an archival X-ray detection of its host galaxy. These observations strongly link PS16dtm to activity associated with the SMBH and are difficult to reconcile with an SN origin or known forms of active galactic nucleus (AGN) variability. Therefore, we argue that PS16dtm is a tidal disruption event (TDE) in which the accretion of the stellar debris powers the rise in the continuum and excitation of the preexisting broad-line region, while obscuring the X-ray-emitting region of the preexisting AGN disk. We predict that PS16dtm will remain bright for years and that the X-ray emission will reappear on a similar timescale as the accretion rate declines. Placing PS16dtm in the context of other TDEs, we find that TDEs in AGN galaxies are more efficient and reach Eddington luminosities, likely due to interaction of the stellar debris with the preexisting accretion disk.