We have observed extraordinarily large optical nonlinearity in Methyl Red-doped nematic liquid-crystal film. Grating diffraction can be generated with an optical intensity as low as 40 microW/cm(2) , and a refractive-index change coefficient of more than 6 cm(2)/ W is obtained. The effect is attributed to formation of an optically induced dc space-charge field and to the resulting reorientation of the highly birefringent nematic director axis.