The co-evolution of a supermassive black hole with its host galaxy1 through cosmic time is encoded in its spin(2-4). At z > 2, supermassive black holes are thought to grow mostly by merger-driven accretion leading to high spin. It is not known, however, whether below z approximate to 1 these black holes continue to grow by coherent accretion or in a chaotic manner(5), though clear differences are predicted(3,4) in their spin evolution. An established method(6) of measuring the spin of black holes is through the study of relativistic reflection features(7) from the inner accretion disk. Owing to their greater distances from Earth, there has hitherto been no significant detection of relativistic reflection features in a moderate-redshift quasar. Here we report an analysis of archival X-ray data together with a deep observation of a gravitationally lensed quasar at z = 0.658. The emission originates within three or fewer gravitational radii from the black hole, implying a spin parameter (a measure of how fast the black hole is rotating) of a = 0.87(-0.15)(0. 08) at the 3 sigma confidence level and a > 0.66 at the 5 sigma level. The high spin found here is indicative of growth by coherent accretion for this black hole, and suggests that black-hole growth at 0.5 <= z <= 1 occurs principally by coherent rather than chaotic accretion episodes.