  We obtain the detailed Feynman rules for perturbative gauge theory on a fixed
Yang-Mills plane wave background. Using these rules, the tree-level 4-point
gluon amplitude is computed and some 1-loop Feynman diagrams are considered. As
an application, we test the extent to which colour-kinematics duality, the
relation between the colour and kinematic constituents of the amplitude, holds
on the plane wave background. Although the duality is obstructed, the
obstruction has an interesting constrained structure. This plane wave version
of colour-kinematics duality reduces on a flat background to the well-known
identities underpinning the BCJ relations for colour-ordered partial
amplitudes, and constrains representations of tree-level amplitudes beyond
4-points.
