We present the discovery of an extreme flaring event from Proxima Cen by ASKAP, ALMA, HST, TESS, and the du Pont Telescope that occurred on 2019 May 1. In the millimeter and FUV, this flare is the brightest ever detected, brightening by a factor of >1000 and >14000 as seen by ALMA and HST, respectively. The millimeter and FUV continuum emission trace each other closely during the flare, suggesting that millimeter emission could serve as a proxy for FUV emission from stellar flares and become a powerful new tool to constrain the high-energy radiation environment of exoplanets. Surprisingly, optical emission associated with the event peaks at a much lower level with a time delay. The initial burst has an extremely short duration, lasting for <10 sec. Taken together with the growing sample of millimeter M dwarf flares, this event suggests that millimeter emission is actually common during stellar flares and often originates from short burst-like events.