[Abridged] We present observations of PS16dtm, a luminous transient that occurred at the nucleus of a known Narrow-line Seyfert 1 galaxy hosting a 10$^6$ M$_odot$ black hole. The transient was previously claimed to be a Type IIn SLSN due to its luminosity and hydrogen emission lines. The light curve shows that PS16dtm brightened by about two magnitudes in ~50 days relative to the archival host brightness and then exhibited a plateau phase for about 100 days followed by the onset of fading in the UV. During the plateau PS16dtm showed no color evolution, maintained a blackbody temperature of 1.7 x 10$^4$ K, and radiated at approximately $L_{Edd}$ of the SMBH. The spectra exhibit multi-component hydrogen emission lines and strong FeII emission, show little evolution with time, and closely resemble the spectra of NLS1s while being distinct from those of Type IIn SNe. 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 a SN origin or any known form of AGN variability, and therefore we argue that it is a TDE in which the accretion of the stellar debris powers the rise in the continuum and excitation of the pre-existing broad line region, while providing material that obscures the X-ray emitting region of the pre-existing AGN accretion disk. A detailed TDE model fit to the light curve indicates that PS16dtm will remain bright for several years; we further predict that the X-ray emission will reappear on a similar timescale as the accretion rate declines. Finally, we place PS16dtm in the context of other TDEs and find that TDEs in AGN galaxies are an order of magnitude more efficient and reach Eddington luminosities, likely due to interaction of the stellar debris with the pre-existing accretion disk.
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