  A star cluster in a galactic nucleus sinks toward the galactic center due to
dynamical friction. As it spirals inward, the cluster loses mass due to stellar
evolution, relaxation driven evaporation, and tidal stripping, eventually
dissolving in the galactic tidal field. We model the inspiral of dense young
star clusters near the center of our Galaxy to study the extent of the region
of parameter space in which the cluster can reach the inner parsec of the
Galaxy within a few million years. Since we neglect changes in cluster
structure due to internal evolution, the present study is most applicable to
star clusters less than about one initial relaxation time old. We find that
only star clusters with initial masses $\apgt 10^5$ {\msun} can reach the
Galactic center from an initial distance of $\apgt 60$ pc within one initial
relaxation time or a few million years, whichever is smaller.
