  The co-evolution of a supermassive black hole with its host galaxy through
cosmic time is encoded in its spin. At $z>2$, supermassive black holes are
thought to grow mostly by merger-driven accretion leading to high spin.
However, it is unknown whether below $z\sim1$ these black holes continue to
grow via coherent accretion or in a chaotic manner, though clear differences
are predicted in their spin evolution. An established method to measure the
spin of black holes is via the study of relativistic reflection features from
the inner accretion disk. Owing to their greater distances, there has hitherto
been no significant detection of relativistic reflection features in a
moderate-redshift quasar. Here, we use archival data together with a new, deep
observation of a gravitationally-lensed quasar at $z=0.658$ to rigorously
detect and study reflection in this moderate-redshift quasar. The level of
relativistic distortion present in this reflection spectrum enables us to
constrain the emission to originate within $\lesssim3$ gravitational radii from
the black hole, implying a spin parameter $a=0.87^{+0.08}_{-0.15} $ at the
$3\sigma$ level of confidence and $a>0.66$ at the $5\sigma$ level. The high
spin found here is indicative of growth via coherent accretion for this black
hole, and suggests that black hole growth between $0.5\lesssim z \lesssim 1$
occurs principally by coherent rather than chaotic accretion episodes.
