In this Letter, we report the discovery of a new dwarf satellite to the Milky Way, located at ($alpha_{2000}, delta_{2000}$) $=$ (158.72,51.92) in the constellation of Ursa Major. This object was detected as an overdensity of red, resolved stars in Sloan Digital Sky Survey data. The color-magnitude diagram of the Ursa Major dwarf looks remarkably similar to that of Sextans, the lowest surface brightness Milky Way companion known, but with approximately an order of magnitude fewer stars. Deeper follow-up imaging confirms this object has an old and metal-poor stellar population and is $sim$ 100 kpc away. We roughly estimate M$_V =$ -6.75 and $r_{1/2} =$ 250 pc for this dwarf. Its luminosity is several times fainter than the faintest known Milky Way dwarf. However, its physical size is typical for dSphs. Even though its absolute magnitude and size are presently quite uncertain, Ursa Major is likely the lowest luminosity and lowest surface brightness galaxy yet known.
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