We report on the discovery of a source that exhibits over 300% amplitude changes in radio flux density on the period of hours. This source, J1819+3845, is the most extremely variable extragalactic source known in the radio sky. We believe these properties are due to interstellar scintillation and show that the source must emit at least 55% of its flux density within a radius of fewer than 16 µas at 5 GHz. The apparent brightness temperature is greater than 5x1012 K, and the source may be explained by a relativistically moving source with a Doppler factor of approximately 15. The scattering occurs predominantly in material only a few tens of parsecs from the Earth, which explains its unusually rapid variability. If the source PKS 0405-385 is similarly affected by local scattering material, Doppler factors of approximately 1000 are not required to explain this source. The discovery of a second source whose properties are well modeled by interstellar scintillation strengthens the argument for this as the cause for much of the variation seen in intraday variables.