  We report the discovery of a remarkable ultra-compact dwarf galaxy around the
massive Virgo elliptical galaxy NGC 4649 (M60), which we term M60-UCD1. With a
dynamical mass of 2.0 x 10^8 M_sun but a half-light radius of only ~ 24 pc,
M60-UCD1 is more massive than any ultra-compact dwarfs of comparable size, and
is arguably the densest galaxy known in the local universe. It has a
two-component structure well-fit by a sum of Sersic functions, with an
elliptical, compact (r_h=14 pc; n ~ 3.3) inner component and a round,
exponential, extended (r_h=49 pc) outer component. Chandra data reveal a
variable central X-ray source with L_X ~ 10^38 erg/s that could be an active
galactic nucleus associated with a massive black hole or a low-mass X-ray
binary. Analysis of optical spectroscopy shows the object to be old (~> 10 Gyr)
and of solar metallicity, with elevated [Mg/Fe] and strongly enhanced [N/Fe]
that indicates light element self-enrichment; such self-enrichment may be
generically present in dense stellar systems. The velocity dispersion (~ 70
km/s) and resulting dynamical mass-to-light ratio (M/L_V=4.9 +/- 0.7) are
consistent with---but slightly higher than---expectations for an old,
metal-rich stellar population with a Kroupa initial mass function. The presence
of a massive black hole or a mild increase in low-mass stars or stellar
remnants is therefore also consistent with this M/L_V. The stellar density of
the galaxy is so high that no dynamical signature of dark matter is expected.
However, the properties of M60-UCD1 suggest an origin in the tidal stripping of
a nucleated galaxy with M_B ~ -18 to -19.
