  The vanishing of the cross section for particular points in phase space -
radiation zeros - is examined for the process $ q \bar q \to W^+W^- \gamma$ at
high energy. Unlike the process $q \bar q' \to W^\pm \gamma$, actual zeros only
occur in the soft-photon limit. However, for photon energies that are not too
large, the cross section does exhibit deep dips in regions of phase space
corresponding to the position of the actual zeros. We show that in these
regions the sensitivity to possible anomalous quartic couplings is very large.
