  A gravitational wave traversing the line of sight to a distant source
produces a frequency shift which contributes to redshift space distortion. As a
consequence, gravitational waves are imprinted as density fluctuations in
redshift space. The gravitational wave contribution to the redshift space power
spectrum. has a different \mu dependence as compared to the dominant
contribution from peculiar velocities. This allows the two signals to be
separated. The prospect of a detection is most favourable at the highest
observable redshift z. Observations of redshifted 21-cm radiation from neutral
hydrogen (HI) hold the possibility of probing very high redshifts. We consider
the possibility of detecting primordial gravitational waves using the redshift
space HI power spectrum. However, we find that the gravitational wave signal,
though present, will not be detectable on super-horizon scales because of
cosmic variance and on sub-horizon scales where the signal is highly
suppressed.
