The magnetic field pervading our Galaxy is a crucial constituent of the interstellar medium: it mediates the dynamics of interstellar clouds, the energy density of cosmic rays, and the formation of stars. The field associated with ionized interstellar gas has been determined through observations of pulsars in our Galaxy. Radio-frequency measurements of pulse dispersion and the rotation of the plane of linear polarization, that is, Faraday rotation, yield an average value for the magnetic field of B approximately 3 microG (ref. 2). The possible detection of Faraday rotation of linearly polarized photons emitted by high-redshift quasars suggests similar magnetic fields are present in foreground galaxies with redshifts z > 1. As Faraday rotation alone, however, determines neither the magnitude nor the redshift of the magnetic field, the strength of galactic magnetic fields at redshifts z > 0 remains uncertain. Here we report a measurement of a magnetic field of B approximately 84 microG in a galaxy at z = 0.692, using the same Zeeman-splitting technique that revealed an average value of B = 6 microG in the neutral interstellar gas of our Galaxy. This is unexpected, as the leading theory of magnetic field generation, the mean-field dynamo model, predicts large-scale magnetic fields to be weaker in the past rather than stronger.