We study the sudden optical and ultraviolet (UV) brightening of 1ES1927+654, which until now was known as a narrow-line active galactic nucleus (AGN). 1ES 1927+654 was part of the small and peculiar class of "true Type-2" AGNs that lack broad emission lines and line-of-sight obscuration. Our high-cadence spectroscopic monitoring captures the appearance of a blue, featureless continuum, followed several weeks later by the appearance of broad Balmer emission lines. This timescale is generally consistent with the expected light travel time between the central engine and the broadline emission region in (persistent) broadline AGN. Hubble Space Telescope spectroscopy reveals no evidence for broad UV emission lines (e.g., CIV{lambda}1549, CIII]{lambda}1909, MgII{lambda}2798), probably owing to dust in the broadline emission region. To the best of our knowledge, this is the first case where the lag between the change in continuum and in broadline emission of a "changing look" AGN has been temporally resolved. The nature and timescales of the photometric and spectral evolution disfavor both a change in line-of-sight obscuration and a change of the overall rate of gas inflow as driving the drastic spectral transformations seen in this AGN. Although the peak luminosity and timescales are consistent with those of tidal disruption events seen in inactive galaxies, the spectral properties are not. The X-ray emission displays a markedly different behavior, with frequent flares on timescales of hours to days, and will be presented in a companion publication.