  The turnover, or peak, magnitude in a galaxy's globular cluster luminosity
function (GCLF) may provide a standard candle for an independent distance
estimator. Here we examine the GCLF of the giant elliptical NGC 4365 using
photometry of ~ 350 globular clusters from the HST's WFPC2. The WFPC2 data have
several advantages over equivalent ground--based imaging. The membership of NGC
4365 in the Virgo cluster has been the subject of recent debate. We have fit a
Gaussian and t_5 profile to the GCLF and find that it can be well represented
by a turnover magnitude of m_V^0 = 24.2 +/- 0.3 and a dispersion sigma = 1.28
+/- 0.15. After applying a small metallicity correction to the `universal'
globular cluster turnover magnitude, we derive a distance modulus of (m -- M) =
31.6 +/- 0.3 which is in reasonable agreement with that from surface brightness
fluctuation measurements. This result places NGC 4365 about 6 Mpc beyond the
Virgo cluster core. For a V_{CMB} = 1592 +/- 24 km/s the Hubble constant is H_o
= 72 (-12,+10) km/s/Mpc. We also describe our method for estimating a local
specific frequency for the GC system within the central 5 h^{-1} kpc which has
fewer uncertain corrections than a total estimate. The resulting value of 6.4
$\pm$ 1.5 indicates that NGC 4365 has a GC richness similar to other early type
galaxies.
