A coherent, sinusoidal peculiar velocity field of 0.003 amplitude and wavelength of 128/h Mpc could explain the apparent redshift periodicity seen in the recent pencil-beam survey of Broadhurst et al. (1990). Such a peculiar velocity field could arise if the power spectrum of density perturbations has a strong feature at about this wavelength. This explanation has additional predictions: the phase, period, and strength of the periodicity should vary in different directions; the strength of the periodicity should decrease at higher redshifts; and there should be more 'thin' structures perpendicular to the line of sight than parallel to it.