We report on continuous-wave and subnanosecond passively Q-switched laser oscillation from a NdAl3(BO3)4 microchip laser operating at 1.06 microm. Efficient and stable laser operation is possible only when resonant pumping (4I9/2-->4F3/2 at 882 nm) is used instead of the traditional 4I9/2-->4F5/2 (808 nm) pumping. The improvement in laser performance is caused by a strong reduction in the pump-induced thermal loading, which is achieved by pumping directly into the emitting level.