We report the discovery of three large (R29 >~ 1 arcminute) extremely low surface brightness (mu_(V,0) ~ 27.0) galaxies identified using our deep, wide-field imaging of the Virgo Cluster from the Burrell Schmidt telescope. Complementary data from the Next Generation Virgo Cluster Survey do not resolve red giant branch stars in these objects down to i=24, yielding a lower distance limit of 2.5 Mpc. At the Virgo distance, these objects have half-light radii 3-10 kpc and luminosities L_V=2-9x10^7 Lsun. These galaxies are comparable in size but lower in surface brightness than the large ultradiffuse LSB galaxies recently identified in the Coma cluster, and are located well within Virgos virial radius; two are projected directly on the cluster core. One object appears to be a nucleated LSB in the process of being tidally stripped to form a new Virgo ultracompact dwarf galaxy. The others show no sign of tidal disruption, despite the fact that such objects should be most vulnerable to tidal destruction in the cluster environment. The relative proximity of Virgo makes these objects amenable to detailed studies of their structural properties and stellar populations. They thus provide an important new window onto the connection between cluster environment and galaxy evolution at the extremes.
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