The Z Cam-type dwarf nova AT Cancri (AT Cnc) displays a classical nova (CN) shell, demonstrating that mass transfer in cataclysmic binaries decreases substantially after a CN eruption. The hibernation scenario of cataclysmic binaries predicts such a decrease, on a time-scale of a few centuries. In order to measure the time since AT Cnc's last CN eruption, we have measured the radial velocities of a hundred clumps in its ejecta with SITELLE, Canada-France-Hawaii Telescope's recently commissioned imaging Fourier transform spectrometer. These range from -455 to +490km/s. Coupled with the known distance to AT Cnc of 460pc, the size of AT Cnc's shell, and a simple model of nova ejecta deceleration, we determine that the last CN eruption of this system occurred 330^+135^_-90_yr ago. This is the most rapid transition from a high mass-transfer rate, nova-like variable to a low mass-transfer rate, dwarf nova yet measured, and in accord with the hibernation scenario of cataclysmic binaries. We conclude by noting the similarity in the deduced outburst date (within a century of 1686 CE) of AT Cnc to a 'guest star' reported in the constellation Cancer by Korean observers in 1645 CE.