  We present all-multiplicity formulae for the tree-level scattering of gluons
and gravitons in the maximal helicity violating (MHV) helicity configuration,
calculated in certain chiral strong fields. The strong backgrounds we consider
are self-dual plane waves in gauge theory and general relativity, which are
treated exactly and admit a well-defined S-matrix. The gauge theory
background-coupled MHV amplitude is simply a dressed analogue of the familiar
Parke-Taylor formula, but the gravitational version has non-trivial new
structures due to graviton tails. Both formulae have just one residual integral
rather than the $n-2$ expected at $n$-points from space-time perturbation
theory; this simplification arises from the integrability of self-dual
backgrounds and their corresponding twistor description. The resulting formulae
pass several consistency checks and limit to the well-known expressions for MHV
scattering of gluons and gravitons when the background becomes trivial.
