  Thanks to the MUSE integral field spectrograph on the VLT, extragalactic
distance measurements with the [O III] 5007 A planetary nebula luminosity
function (PNLF) are now possible out to approx. 40 Mpc. Here we analyze the
VLT/MUSE data for 20 galaxies from the ESO public archive to identify the
systems' planetary nebulae (PNe) and determine their PNLF distances. Three of
the galaxies do not contain enough PNe for a robust measure of the PNLF, and
the results for one other system are compromised by the galaxy's internal
extinction. However, we obtain robust PNLF distances for the remaining 16
galaxies, two of which are isolated and beyond 30 Mpc in a relatively
unperturbed Hubble flow. From these data, we derive a Hubble Constant of 74.2
+/- 7.2 (stat) +/-3.7 (sys) km/s/Mpc, a value that is very similar to that
found from other quality indicators (e.g., Cepheids, the tip of the red giant
branch, and surface brightness fluctuations). At present, the uncertainty is
dominated by the small number of suitable galaxies in the ESO archival and
their less than ideal observing conditions and calibrations. Based on our
experience with these systems, we identify the observational requirements
necessary for the PNLF to yield a competitive value for H0 that is independent
of the SN Ia distance scale, and help resolve the current tension in the Hubble
constant.
