Cometary outgassing can produce torques that change the spin state of the nucleus, influencing the evolution and lifetimes of comets (1,2). If these torques spin up the rotation to the point that centripetal forces exceed the material strength of the nucleus, the comet may fragment (3). Torques that slow down the rotation can cause the spin state to become unstable, but if the torques persist, the nucleus may eventually reorient itself and start to spin up again (4). Simulations predict that most comets will go through a short phase of changing spin states, after which changes occur gradually over long times (5). We report on observations of comet 41P/Tuttle-Giacobini-Kresak during its highly favourable close approach to Earth (0.142 au on April 1, 2017) that reveal a dramatic spin-down. Between March and May 2017, the nucleus apparent rotation period increased from 20 hours to over 46 hours, reflecting a rate of change more than an order of magnitude larger than has ever been measured before. This phenomenon must be caused by a fortuitous alignment of the comets gas emission in such a way as to produce an anomalously strong torque that is slowing the nucleus spin rate. The behaviour of 41P suggests that it is in a distinct evolutionary state and that its rotation may be approaching the point of instability.