We have fabricated high-Q photonic crystal nanocavities with a lateral p-i-n structure to demonstrate low-power and high-speed electro-optic modulation in a silicon chip. GHz operation is demonstrated at a very low (microW level) operating power, which is about 4.6 times lower than that reported for other cavities in silicon. This low-power operation is due to the small size and high-Q of the photonic crystal nanocavity.