Almost a century since the dawn of general relativity, we have yet to obtain direct evidence of one of its key predictions: gravitational waves. In this lecture, I will point out how the precisely regular vibrations of atoms in optical atomic clocks can be used to detect the minuscule ripples in time due to gravitational waves. This approach requires portable atomic clocks with high sensitivity and reliable performance. I will describe one approach to realizing such clocks, and lay out the prospects for gravitational wave imaging and astronomy using arrays of satellite-borne clocks. These detectors would complement the efforts to detect gravitational waves using terrestrial (Michelson) interferometers, and open up an exciting new window into the gravitational machinery of the universe.