  We show that the solutions of the three-dimensional critical defocusing
nonlinear wave equation with Neumann boundary conditions outside a ball and
radial initial data scatter. This is to our knowledge the first result of
scattering for a nonlinear wave equation with Neumann boundary conditions. Our
proof uses the scheme of concentration-compactness/rigidity introduced by Kenig
and Merle, extending it to our setup, together with the so-called channels of
energy method to rule out compact-flow solutions. We also obtain, for the
focusing equation, the same exact scattering/blow-up dichotomy below the energy
of the ground-state as in $\mathbb R^3$.
