We report on the results of multiwavelength follow-up observations with Gemini, Very Large Array (VLA), and Australia Telescope Compact Array 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 × 1032 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 ∼ 2′ × 2′. 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, 14 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 μJy beam-1 and 22.1 μJy 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 Hα 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.