We present time series of ultra-high S/N, high-resolution spectra of t
he He II 4686 Angstrom emission line in the O4I(n)f supergiant zeta Pu
ppis, the brightest early-type O star in the sky. These reveal stochas
tic variable substructures in the line, which tend to move away from t
he line center with time. Similar scaled-up features are well establis
hed in the strong winds of Wolf-Rayet stars (the presumed descendants
of O stars), where they are explained by outward-moving inhomogeneitie
s (e.g., blobs, clumps, and shocks) in the winds. If all hot star wind
s are dumped like that of zeta Pup, as is plausible, then mass loss ra
tes based on recombination-line intensities will have to be revised do
wnward. Using a standard ''beta'' velocity law, we deduce a value of b
eta = 1.0-1.2 to account for the kinematics of these structures in the
wind of zeta Pup. In addition to the small-scale stochastic variation
s, we also find a slow systematic variation of the mean central absorp
tion reversal.