  Atomic clocks have recently reached a fractional timing precision of
$<10^{-18}$. We point out that an array of atomic clocks, distributed along the
Earth's orbit around the Sun, will have the sensitivity needed to detect the
time dilation effect of mHz gravitational waves (GWs), such as those emitted by
supermassive black hole binaries at cosmological distances. Simultaneous
measurement of clock-rates at different phases of a passing GW provides an
attractive alternative to the interferometric detection of temporal variations
in distance between test masses separated by less than a GW wavelength,
currently envisioned for the eLISA mission.
