We report what we believe to be the first demonstration of a Kerr-lens mode-locked Cr(3+):LiSrAlF(6)laser that is pumped by a single narrow-stripe AlGaInP laser diode with a diffraction-limited output beam. A novel low-loss three-mirror laser cavity design is described in which strong, localized Kerr lensing was exploited such that 75-fs-duration pulses were obtained for only 36mW of incident pump power. This pump power was maintained for 18h by just three AA batteries as the electrical power source. We have shown that mode locking can be sustained for pump powers as low as 22mW.