  We have used the NASA Infra-Red Telescope Facility (IRTF) to observe the
nuclear stellar cluster in the nearby, face-on, giant Scd spiral IC 342. From
high resolution (R = 21500) spectra at the 12CO (2-0) bandhead at 2.3 micron we
derive a line-of-sight stellar velocity dispersion sigma = (33 +- 3) km/s.
  To interpret this observation we construct dynamical models based on the
Jeans equation for a spherical system. The light distribution of the cluster is
modeled using an isophotal analysis of an HST V-band image from the HST Data
Archive, combined with new ground-based K-band imaging. Under the assumption of
an isotropic velocity distribution, the observed kinematics imply a K-band
mass-to-light ratio M/L_K = 0.05, and a cluster mass M ~ 6 times 10^6 Msun. We
model the mass-to-light ratio with the `starburst99' stellar population
synthesis models of Leitherer and collaborators, and infer a best-fitting
cluster age in the range 63-630 Myears. Although this result depends somewhat
on a number of uncertainties in the modeling (e.g., the assumed extinction
along the line-of-sight towards the nucleus, the IMF of the stellar population
model, and the velocity dispersion anisotropy of the cluster), none of these
can be plausibly modified to yield a significantly larger age. We discuss the
implications of this result on possible scenarios for the frequency of nuclear
starbursts and their impact on secular evolution of spiral galaxy nuclei.
  As a byproduct of our analysis, we infer that IC 342 cannot have any central
black hole more massive than 0.5 million solar masses. This is ~ 6 times less
massive than the black hole inferred to exist in our Galaxy, consistent with
the accumulating evidence that galaxies with less massive bulges harbor less
massive black holes.
