Anomalously fast ion heating has been observed in the Caltech Encore tokamak [Phys. Rev. Lett. 59, 1436 (1987)], with the use of laser-induced fluorescence. This heating was found to be independent of electron temperature, but was well correlated with the presence of large-amplitude drift-Alfven waves. Evidence is presented that suggests that the heating is stochastic and occurs when the ion displacement due to polarization drift becomes comparable to the perpendicular wavelength, i.e., when k perpendicular-to (m(i)k perpendicular-to phi0/qB2) approximately 1. Stochastic heating may also be the cause of the anomalously high ion temperatures observed in reversed-field pinches.