Relativistic (>1 MeV) 'killer electrons' are frequently generated in the Earth's inner magnetosphere during the recovery phase of a typical magnetic storm. We test the hypothesis that the energization of electrons takes place by means of stochastic gyroresonant interaction between lower-energy (several 100 keV) seed electrons and whistler-mode chorus waves. We develop a model kinetic equation for the electron energy distribution, and utilize both electron and whistler-mode wave data at L = 4 for a typical geomagnetic storm (on October 9, 1990) from instruments carried on the Combined Release and Radiation Effects Satellite (CRRES). Our model solutions are found to match well with the CRRES profiles of the electron flux. We conclude that the mechanism of stochastic acceleration by whistler-mode turbulence is a viable candidate for generating killer electrons, not only for the storm considered, but for similar storms with a several-day recovery phase containing prolonged substorm activity.