  We report on the results of multi-wavelength follow-up observations with
Gemini, VLA, and ATCA, to search for a host galaxy and any persistent radio
emission associated with FRB 180309. This FRB is among the most luminous FRB
detections to date, with a luminosity of $> 8.7\times 10^{32}$ erg Hz$^{-1}$ at
the dispersion-based redshift upper limit of 0.32. We used the
high-significance detection of FRB 180309 with the Parkes Telescope and a beam
model of the Parkes Multibeam Receiver to improve the localization of the FRB
to a region spanning approximately $\sim2'\times2'$. We aimed to seek bright
galaxies within this region to determine the strongest candidates as the
originator of this highly luminous FRB. We identified optical sources within
the localization region above our r-band magnitude limit of 24.27, fourteen of
which have photometric redshifts whose fitted mean is consistent with the
redshift upper limit ($z < 0.32$) of our FRB. Two of these galaxies are
coincident with marginally detected "persistent" radio sources of flux density
24.3$\mu$Jy beam$^{-1}$ and 22.1$\mu$Jy beam$^{-1}$ respectively. Our
redshift-dependent limit on the luminosity of any associated persistent radio
source is comparable to the luminosity limits for other localized FRBs. We
analyze several properties of the candidate hosts we identified, including
chance association probability, redshift, and presence of radio emission,
however it remains possible that any of these galaxies could be the host of
this FRB. Follow-up spectroscopy on these objects to explore their H$\alpha$
emission and ionization contents, as well as to obtain more precisely measured
redshifts, may be able to isolate a single host for this luminous FRB.
