  We introduce a Chern-Simons Lagrangian for Yang-Mills theory as formulated on
ambitwistor space via the Ward, Isenberg, Yasskin, Green, Witten construction.
The Lagrangian requires the selection of a codimension-2 Cauchy-Riemann
submanifold which is naturally picked out by the choice of space-time reality
structure and we focus on the choice of Euclidean signature. The action is
shown to give rise to a space-time action that is equivalent to the standard
one, but has just cubic vertices. We identify the ambitwistor propagators and
vertices and work out their corresponding expressions on space-time and
momentum space. It is proposed that this formulation of Yang-Mills theory
underlies the recursion relations of Britto, Cachazo, Feng and Witten and
provides the generating principle for twistor diagrams for gauge theory.
