  Intense, millisecond-duration bursts of radio waves have been detected from
beyond the Milky Way [1]. Their extragalactic origins are evidenced by their
large dispersion measures, which are greater than expected for propagation
through the Milky Way interstellar medium alone, and imply contributions from
the intergalactic medium and potentially host galaxies [2]. Although several
theories exist for the sources of these fast radio bursts, their intensities,
durations and temporal structures suggest coherent emission from highly
magnetised plasma [3,4]. Two sources have been observed to repeat [5,6], and
one repeater (FRB 121102) has been localised to the largest star-forming region
of a dwarf galaxy at a cosmological redshift of 0.19 [7, 8]. However, the host
galaxies and distances of the so far non-repeating fast radio bursts are yet to
be identified. Unlike repeating sources, these events must be observed with an
interferometer with sufficient spatial resolution for arcsecond localisation at
the time of discovery. Here we report the localisation of a fast radio burst
(FRB 190523) to a few-arcsecond region containing a single massive galaxy at a
redshift of 0.66. This galaxy is in stark contrast to the host of FRB 121102,
being a thousand times more massive, with a greater than hundred times lower
specific star-formation rate. The properties of this galaxy highlight the
possibility of a channel for FRB production associated with older stellar
populations.
