  Recent high-resolution observations with the Hubble Space Telescope (HST)
reveal that star clusters of extraordinary luminosity and compactness are
commonly found in a variety of starburst systems. There has been much
speculation that these clusters represent present-day analogs of young globular
clusters. Using the HIRES echelle spectrograph on the Keck 10 m telescope, we
obtained high-dispersion optical spectra of one of the ``super star clusters''
(cluster ``A'') in the nearby dwarf galaxy NGC 1569. The size of the cluster is
known from published HST images. The line-of-sight velocity dispersion
(15.7+-1.5 km/s) has been measured from a cross-correlation analysis of its
integrated spectrum at visual wavelengths. If the cluster is gravitationally
bound and the velocities are isotropic, application of the virial theorem
implies that the cluster has a total stellar mass of (3.3+-0.5) X 10$^5$ solar
masses. This object's mass, mass density, and probable mass-to-light ratio
after aging 10--15 Gyr are fully consistent with the typical values of Galactic
globular clusters. Our result strongly suggests that at least some of the
luminous, compact, young star clusters being discovered with {\it HST} will
indeed evolve into normal globular clusters of the type seen in the Milky Way.
