  In this Letter, we study a localized stellar overdensity in the constellation
of Ursa Major, first identified in Sloan Digital Sky Survey (SDSS) data and
subsequently followed up with Subaru imaging. Its color-magnitude diagram (CMD)
shows a well-defined sub-giant branch, main sequence and turn-off, from which
we estimate a distance of ~30 kpc and a projected size of ~250 x 125 pc. The
CMD suggests a composite population with some range in metallicity and/or age.
Based on its extent and stellar population, we argue that this is a previously
unknown satellite galaxy of the Milky Way, hereby named Ursa Major II (UMa II)
after its constellation. Using SDSS data, we find an absolute magnitude of M_V
\~ -3.8, which would make it the faintest known satellite galaxy. UMa II's
isophotes are irregular and distorted with evidence for multiple
concentrations; this suggests that the satellite is in the process of
disruption.
