Yes, but there's only as many free electrons as the capacitance and original charge of the chip allows. Say, you're 10KV away from the chip potential. By touching it, you inject/remove enough electrons to charge it to that 10KV and since chips usually have quite low capacitance, that's not much. Of course it happens really fast, so pretty high current crosses the chip, but because it happens so fast there's not much energy created. It still can damage a chip, but the chance is far lower if all the charge stored in you would cross it.

BTW, what is the capacitance of a human body?