  The Brillouin action is a Wilson-like lattice fermion action with a 81-point
stencil, which was found to ameliorate the Wilson action in many respects. The
Sheikholeslami-Wohlert coefficient $c_\mathrm{SW}$ of the clover improvement
term has a perturbative expansion
$c_\mathrm{SW}=c_\mathrm{SW}^{(0)}+g_0^2c_\mathrm{SW}^{(1)}+\mathcal{O}(g_0^4)$.
At tree-level $c_\mathrm{SW}^{(0)}=r$ holds for Wilson and Brillouin fermions
alike. We present the Feynman rules for the Brillouin action in lattice
perturbation theory, and employ them to calculate the one-loop coefficient
$c_\mathrm{SW}^{(1)}$ with plaquette or L\"uscher-Weisz gluons. Numerically its
value is found to be about half that of the Wilson action.
