  We present the results of an intensive photometric and spectroscopic
monitoring campaign of the WN4 Wolf-Rayet (WR) star WR1=HD4004. Our broadband V
photometry covering a timespan of 91 days shows variability with a period of
P=16.9$^{+0.6}_{-0.3}$ days. The same period is also found in our spectral
data. The light-curve is non-sinusoidal with hints of a gradual change in its
shape as a function of time. The photometric variations nevertheless remain
coherent over several cycles and we estimate that the coherence timescale of
the light-curve is of the order of 60 days. The spectroscopy shows large-scale
line-profile variability which can be interpreted as excess emission peaks
moving from one side of the profile to the other on a timescale of several
days. Although we cannot unequivocally exclude the unlikely possibility that
WR1 is a binary, we propose that the nature of the variability we have found
strongly suggests that it is due to the presence in the wind of the WR star of
large-scale structures, most likely Co-rotating Interaction Regions (CIRs),
which are predicted to arise in inherently unstable radiatively driven winds
when they are perturbed at their base. We also suggest that variability
observed in WR6, WR134 and WR137 is of the same nature. Finally, assuming that
the period of CIRs is related to the rotational period, we estimate the
rotation rate of the four stars for which sufficient monitoring has been
carried out; i.e. v$_{rot}$=6.5, 40, 70 and 275 km/s for WR1, WR6, WR134 and
WR137, respectively.
