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Fast Radio Bursts (FRBs) are brief radio emissions from distant astronomical sources. Some are known to repeat, but most are single bursts. Non-repeating FRB observations have had insufficient positional accuracy to localize them to an individual host galaxy. We report the interferometric localization of the single pulse FRB 180924 to a position 4 kpc from the center of a luminous galaxy at redshift 0.3214. The burst has not been observed to repeat. The properties of the burst and its host are markedly different from the only other accurately localized FRB source. The integrated electron column density along the line of sight closely matches models of the intergalactic medium, indicating that some FRBs are clean probes of the baryonic component of the cosmic web.Cosmological observations have shown that baryons comprise 4% of the energy density of the Universe, of which only about 10% is in cold gas and stars (1), with the remainder residing in a diffuse plasma surrounding and in between galaxies and galaxy clusters. The location and density of this material has been challenging to characterize, and up to 50% of it remains unaccounted (2).Fast radio bursts (FRBs; ref.(3)) are bright bursts of radio waves with millisecond duration. They can potentially be used to detect, study, and map this medium, as bursts of emission are dispersed and scattered by their 1 arXiv:1906.11476v1 [astro-ph.HE] 27 Jun 2019 dual-polarization beams on the sky using digital beamforming, producing a total field-of-view of ∼ 30 deg 2 . For burst detection, the beamformers produces channelized autocorrelation spectra for both linear polarizations of all beams, with an integration time of 864 µs and channel bandwidth of 1 MHz in these observations. We used 336 channels centered at 1320 MHz. A real-time detection pipeline incoherently adds the spectra from all available antennas (24 antennas in these observations) and polarization channels, then searches (16) the result for dispersed pulses (17).Burst localization is completed with a second data product that utilizes both the amplitude and phase information of the burst radiation. The beamformers store samples of the complex electric field for all beams and both polarizations in a ring buffer of 3.1 s duration, with the oldest data being continuously overwritten by new data. The data are saved for offline interferometric analysis only when the pipeline identifies a candidate. For the searches reported here the triggering required pulses with widths less than 9 ms and S/N > 10.Previous searches with ASKAP used antennas pointed in different directions to maximize sky coverage (10,16). In contrast, our observations used antennas all pointed in the same direction, enabling the array to act as an interferometer capable of sub-arcsecond localization with a 30 deg 2 field of view. We targeted high Galactic latitude fields (Galactic latitude |b| ∼ 50 • ), that had been observed previously (10, 16), and Southern circumpolar fields. The high-latitude fields were observed regularly through 2017 and earl...