  Classical ${\cal N}=4$ Yang-Mills theory is defined by the superspace
constraints. We obtain a solution of a subset of these constraints and show
that it leads to the maximally helicity violating (MHV) amplitudes. The action
which leads to the solvable part of the constraints is a Wess-Zumino-Witten
(WZW) action on a suitably extended superspace. The non-MHV tree amplitudes can
also be expressed in terms of this action.
