The canonical theory for planet formation in circumstellar disks proposes that planets are grown from initially much smaller seeds^1–5. The long-considered alternative theory proposes that giant protoplanets can be formed directly from collapsing fragments of vast spiral arms^6–11 induced by gravitational instability^12–14—if the disk is gravitationally unstable. For this to be possible, the disk must be massive compared with the central star: a disk-to-star mass ratio of 1:10 is widely held as the rough threshold for triggering gravitational instability, inciting substantial non-Keplerian dynamics and generating prominent spiral arms^15–18. Although estimating disk masses has historically been challenging^19–21, the motion of the gas can reveal the presence of gravitational instability through its effect on the disk-velocity structure^22–24. Here we present kinematic evidence of gravitational instability in the disk around AB Aurigae, using deep observations of ¹³CO and C¹⁸O line emission with the Atacama Large Millimeter/submillimeter Array (ALMA). The observed kinematic signals strongly resemble predictions from simulations and analytic modelling. From quantitative comparisons, we infer a disk mass of up to a third of the stellar mass enclosed within 1″ to 5″ on the sky.